Matrix Scalar Multiplication< (with worked solutions & videos)/TITLE> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META name="Description" content="How to multiply a matrix by a scalar"> <META name="Keywords" content="matrices scalar multiplication, matrix, matrix scalar product"> <link href="http://www.onlinemathlearning.com/support-files/oml.css" rel="stylesheet" type="text/css"> </HEAD> <body onload="MM_preloadImages('http://www.onlinemathlearning.com/imgs/index-over.gif', 'http://www.onlinemathlearning.com/imgs/pre-k-over.gif', 'http://www.onlinemathlearning.com/imgs/kindergarten-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-1-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-2-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-3-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-4-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-5-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-6-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-7-over.gif', 'http://www.onlinemathlearning.com/imgs/grade-9-over.gif', 'http://www.onlinemathlearning.com/imgs/arithmetic-over.gif', 'http://www.onlinemathlearning.com/imgs/algebra-help-over.gif', 'http://www.onlinemathlearning.com/imgs/geometry-help-over.gif', 'http://www.onlinemathlearning.com/imgs/statistics-over.gif', 'http://www.onlinemathlearning.com/imgs/math-probability-over.gif', 'http://www.onlinemathlearning.com/imgs/math-sets-over.gif', 'http://www.onlinemathlearning.com/imgs/basic-trigonometry-over.gif', 'http://www.onlinemathlearning.com/imgs/matrices-lessons-over.gif', 'http://www.onlinemathlearning.com/imgs/vectors-over.gif', 'http://www.onlinemathlearning.com/imgs/calculus-help-over.gif', 'http://www.onlinemathlearning.com/imgs/sat-test-prep-over.gif', 'http://www.onlinemathlearning.com/imgs/act-test-prep-over.gif', 'http://www.onlinemathlearning.com/imgs/gmat-test-prep-over.gif', 'http://www.onlinemathlearning.com/imgs/_interactive-over.gif', 'http://www.onlinemathlearning.com/imgs/math-worksheets-over.gif', 'http://www.onlinemathlearning.com/imgs/math-games-over.gif', 'http://www.onlinemathlearning.com/imgs/educational-games-over.gif', 'http://www.onlinemathlearning.com/imgs/math-trivia-over.gif', 'http://www.onlinemathlearning.com/imgs/english-help-over.gif', 'http://www.onlinemathlearning.com/imgs/animal-facts-over.gif', 'http://www.onlinemathlearning.com/imgs/tutoring-over.gif', 'http://www.onlinemathlearning.com/imgs/math-help-blog-over.gif', 'http://www.onlinemathlearning.com/imgs/links-over.gif');" vLink=purple aLink=red link=blue bgColor=#ffffff leftMargin=0 background="http://www.onlinemathlearning.com/imgs/BACK.gif" topMargin=0 marginheight="0" marginwidth="0"> <TABLE cellSpacing=0 cellPadding=0 width=725 align=left border=0> <TBODY> <TR> <TD colSpan=2><IMG src="http://www.onlinemathlearning.com/imgs/logo.gif"></TD> </TR> <TR> <TD vAlign=top width=130 background="http://www.onlinemathlearning.com/imgs/LEFT.gif"><DIV id="Layer1" style="position:absolute; width:130px; z-index:1; top: 120"> <BR> <style type="text/css"> #navheader { display: block; width: 130px; font-family: Verdana; font-size: 14px; font-weight: bold; color: #000000; text-align: left; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; background-color: #FFFFFF } </style> <a href="http://www.onlinemathlearning.com/index.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('index','','http://www.onlinemathlearning.com/imgs/index-over.gif',1)"><img name="index" border="0" src="http://www.onlinemathlearning.com/imgs/index.gif" alt="Home"></a><br> <a href="http://www.onlinemathlearning.com/pre-k.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image0','','http://www.onlinemathlearning.com/imgs/pre-k-over.gif',1)"><img name="Image0" border="0" src="http://www.onlinemathlearning.com/imgs/pre-k.gif" alt="Pre-K"></a><br> <a href="http://www.onlinemathlearning.com/kindergarten.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image1','','http://www.onlinemathlearning.com/imgs/kindergarten-over.gif',1)"><img name="Image1" border="0" src="http://www.onlinemathlearning.com/imgs/kindergarten.gif" alt="Kindergarten"></a><br> <a href="http://www.onlinemathlearning.com/grade-1.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image2','','http://www.onlinemathlearning.com/imgs/grade-1-over.gif',1)"><img name="Image2" border="0" src="http://www.onlinemathlearning.com/imgs/grade-1.gif" alt="Grade 1"></a><br> <a href="http://www.onlinemathlearning.com/grade-2.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image3','','http://www.onlinemathlearning.com/imgs/grade-2-over.gif',1)"><img name="Image3" border="0" src="http://www.onlinemathlearning.com/imgs/grade-2.gif" alt="Grade 2"></a><br> <a href="http://www.onlinemathlearning.com/grade-3.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image4','','http://www.onlinemathlearning.com/imgs/grade-3-over.gif',1)"><img name="Image4" border="0" src="http://www.onlinemathlearning.com/imgs/grade-3.gif" alt="Grade 3"></a><br> <a href="http://www.onlinemathlearning.com/grade-4.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image5','','http://www.onlinemathlearning.com/imgs/grade-4-over.gif',1)"><img name="Image5" border="0" src="http://www.onlinemathlearning.com/imgs/grade-4.gif" alt="Grade 4"></a><br> <a href="http://www.onlinemathlearning.com/grade-5.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image6','','http://www.onlinemathlearning.com/imgs/grade-5-over.gif',1)"><img name="Image6" border="0" src="http://www.onlinemathlearning.com/imgs/grade-5.gif" alt="Grade 5"></a><br> <a href="http://www.onlinemathlearning.com/grade-6.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image7','','http://www.onlinemathlearning.com/imgs/grade-6-over.gif',1)"><img name="Image7" border="0" src="http://www.onlinemathlearning.com/imgs/grade-6.gif" alt="Grade 6"></a><br> <a href="http://www.onlinemathlearning.com/grade-7.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image8','','http://www.onlinemathlearning.com/imgs/grade-7-over.gif',1)"><img name="Image8" border="0" src="http://www.onlinemathlearning.com/imgs/grade-7.gif" alt="Grades 7 and 8"></a><br> <a href="http://www.onlinemathlearning.com/grade-9.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image9','','http://www.onlinemathlearning.com/imgs/grade-9-over.gif',1)"><img name="Image9" border="0" src="http://www.onlinemathlearning.com/imgs/grade-9.gif" alt="Grade 9"></a><br> <a href="http://www.onlinemathlearning.com/arithmetic.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image10','','http://www.onlinemathlearning.com/imgs/arithmetic-over.gif',1)"><img name="Image10" border="0" src="http://www.onlinemathlearning.com/imgs/arithmetic.gif" alt="Arithmetic"></a><br> <a href="http://www.onlinemathlearning.com/algebra-help.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image11','','http://www.onlinemathlearning.com/imgs/algebra-help-over.gif',1)"><img name="Image11" border="0" src="http://www.onlinemathlearning.com/imgs/algebra-help.gif" alt="Algebra"></a><br> <a href="http://www.onlinemathlearning.com/geometry-help.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image12','','http://www.onlinemathlearning.com/imgs/geometry-help-over.gif',1)"><img name="Image12" border="0" src="http://www.onlinemathlearning.com/imgs/geometry-help.gif" alt="Geometry"></a><br> <a href="http://www.onlinemathlearning.com/statistics.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image13','','http://www.onlinemathlearning.com/imgs/statistics-over.gif',1)"><img name="Image13" border="0" src="http://www.onlinemathlearning.com/imgs/statistics.gif" alt="Statistics"></a><br> <a href="http://www.onlinemathlearning.com/math-probability.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image14','','http://www.onlinemathlearning.com/imgs/math-probability-over.gif',1)"><img name="Image14" border="0" src="http://www.onlinemathlearning.com/imgs/math-probability.gif" alt="Probability"></a><br> <a href="http://www.onlinemathlearning.com/math-sets.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image15','','http://www.onlinemathlearning.com/imgs/math-sets-over.gif',1)"><img name="Image15" border="0" src="http://www.onlinemathlearning.com/imgs/math-sets.gif" alt="Set Theory"></a><br> <a href="http://www.onlinemathlearning.com/basic-trigonometry.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image16','','http://www.onlinemathlearning.com/imgs/basic-trigonometry-over.gif',1)"><img name="Image16" border="0" src="http://www.onlinemathlearning.com/imgs/basic-trigonometry.gif" alt="Trigonometry"></a><br> <a href="http://www.onlinemathlearning.com/matrices-lessons.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image17','','http://www.onlinemathlearning.com/imgs/matrices-lessons-over.gif',1)"><img name="Image17" border="0" src="http://www.onlinemathlearning.com/imgs/matrices-lessons.gif" alt="Matrices"></a><br> <a href="http://www.onlinemathlearning.com/vectors.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image18','','http://www.onlinemathlearning.com/imgs/vectors-over.gif',1)"><img name="Image18" border="0" src="http://www.onlinemathlearning.com/imgs/vectors.gif" alt="Vectors"></a><br> <a href="http://www.onlinemathlearning.com/calculus-help.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image19','','http://www.onlinemathlearning.com/imgs/calculus-help-over.gif',1)"><img name="Image19" border="0" src="http://www.onlinemathlearning.com/imgs/calculus-help.gif" alt="Calculus"></a><br> <a href="http://www.onlinemathlearning.com/sat-test-prep.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image20','','http://www.onlinemathlearning.com/imgs/sat-test-prep-over.gif',1)"><img name="Image20" border="0" src="http://www.onlinemathlearning.com/imgs/sat-test-prep.gif" alt="SAT Preparation"></a><br> <a href="http://www.onlinemathlearning.com/act-test-prep.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image21','','http://www.onlinemathlearning.com/imgs/act-test-prep-over.gif',1)"><img name="Image21" border="0" src="http://www.onlinemathlearning.com/imgs/act-test-prep.gif" alt="ACT Preparation"></a><br> <a href="http://www.onlinemathlearning.com/gmat-test-prep.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image22','','http://www.onlinemathlearning.com/imgs/gmat-test-prep-over.gif',1)"><img name="Image22" border="0" src="http://www.onlinemathlearning.com/imgs/gmat-test-prep.gif" alt="GMAT Preparation"></a><br> <a href="http://interactive.onlinemathlearning.com/" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image23','','http://www.onlinemathlearning.com/imgs/_interactive-over.gif',1)" onClick="window.location.href='http://www.onlinemathlearning.com/cgi-bin/counter.pl?url=http%3A%2F%2Finteractive%2Eonlinemathlearning%2Ecom%2F&referrer=http%3A%2F%2Fwww%2Eonlinemathlearning%2Ecom%2Fmatrix-scalar-multiplication%2Ehtml'; return false;"><img name="Image23" border="0" src="http://www.onlinemathlearning.com/imgs/_interactive.gif" alt="Interactive Zone"></a><br> <a href="http://www.onlinemathlearning.com/math-worksheets.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image24','','http://www.onlinemathlearning.com/imgs/math-worksheets-over.gif',1)"><img name="Image24" border="0" src="http://www.onlinemathlearning.com/imgs/math-worksheets.gif" alt="Math Worksheets"></a><br> <a href="http://www.onlinemathlearning.com/math-games.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image25','','http://www.onlinemathlearning.com/imgs/math-games-over.gif',1)"><img name="Image25" border="0" src="http://www.onlinemathlearning.com/imgs/math-games.gif" alt="Math Games"></a><br> <a href="http://www.onlinemathlearning.com/educational-games.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image26','','http://www.onlinemathlearning.com/imgs/educational-games-over.gif',1)"><img name="Image26" border="0" src="http://www.onlinemathlearning.com/imgs/educational-games.gif" alt="Fun Games"></a><br> <a href="http://www.onlinemathlearning.com/math-trivia.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image27','','http://www.onlinemathlearning.com/imgs/math-trivia-over.gif',1)"><img name="Image27" border="0" src="http://www.onlinemathlearning.com/imgs/math-trivia.gif" alt="Math Trivia"></a><br> <a href="http://www.onlinemathlearning.com/english-help.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image28','','http://www.onlinemathlearning.com/imgs/english-help-over.gif',1)"><img name="Image28" border="0" src="http://www.onlinemathlearning.com/imgs/english-help.gif" alt="English Help"></a><br> <a href="http://www.onlinemathlearning.com/animal-facts.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image29','','http://www.onlinemathlearning.com/imgs/animal-facts-over.gif',1)"><img name="Image29" border="0" src="http://www.onlinemathlearning.com/imgs/animal-facts.gif" alt="Animal Facts"></a><br> <a href="http://www.onlinemathlearning.com/tutoring.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image30','','http://www.onlinemathlearning.com/imgs/tutoring-over.gif',1)"><img name="Image30" border="0" src="http://www.onlinemathlearning.com/imgs/tutoring.gif" alt="Tutoring Services"></a><br> <a href="http://www.onlinemathlearning.com/math-help-blog.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image31','','http://www.onlinemathlearning.com/imgs/math-help-blog-over.gif',1)"><img name="Image31" border="0" src="http://www.onlinemathlearning.com/imgs/math-help-blog.gif" alt="What's New"></a><br> <a href="http://www.onlinemathlearning.com/links.html" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('Image32','','http://www.onlinemathlearning.com/imgs/links-over.gif',1)"><img name="Image32" border="0" src="http://www.onlinemathlearning.com/imgs/links.gif" alt="Links"></a><br> <BR> </DIV> <img src="http://www.onlinemathlearning.com/imgs/LEFT.gif"></TD> <TD vAlign=top width=595 background="http://www.onlinemathlearning.com/image-files/main-594-1-right-border.gif"><TABLE cellSpacing=0 cellPadding=8 width=550 border=0> <TBODY> <TR> <TD width=15> </TD>  <TD><h1>Scalar Matrix Multiplication</h1> <p> </p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p> </p> <p>We can multiply a matrix with a number (also called a <strong class="definition">scalar</strong>). For scalar multiplication, we multiply each element of the matrix by the number or scalar. </p> <p class="highlight-example"><strong><em> Example: </em></strong></p> <p><img width="271" height="48" src="http://www.onlinemathlearning.com/image-files/matrices006_0003.gif"></p> <p><img width="345" height="48" src="http://www.onlinemathlearning.com/image-files/matrix-scalar-multiplication1.gif"></p> <p> </p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p> </p> <p class="highlight-example"><strong><em> Example: </em></strong></p> <p><img width="308" height="48" src="http://www.onlinemathlearning.com/image-files/matrices010_0002.gif"></p> <p class="highlight-example"><strong><em> Solution: </em></strong></p> <p> We need to consider only one equation </p> <p> 2k = 6 </p> <p> k = 3 </p> <p> </p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p> </p> <p class="highlight-example"><strong><em> Example</em> : </strong></p> <p> Find the values of x and y. </p> <p><img width="117" height="48" src="http://www.onlinemathlearning.com/image-files/matrices012_0001.gif"></p> <p class="highlight-example"><strong><em> Solution: </em></strong></p> <p> 2<em>x</em> – 6 = 5 <br>2<em>x</em> = 11 <br><em>x</em> = 5.5 </p> <p> 4 –<em> y</em> = 3 <br><em>y</em> = 1 </p> <p> </p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p> </p> <h2>Video</h2> Multiplying matrices by a scalar - <br> Professor Edward Burger explains multiplying matrices by a scalar. <br> <br> <div style='text-align:center'><object width='480' height='401' id='FiveminPlayer' classid='clsid:d27cdb6e-ae6d-11cf-96b8-444553540000'><param name='allowfullscreen' value='true'/><param name='allowScriptAccess' value='always'/><param name='movie' value='http://www.5min.com/Embeded/161027697/'/><embed name='FiveminPlayer' src='http://www.5min.com/Embeded/161027697/' type='application/x-shockwave-flash' width='480' height='401' allowfullscreen='true' allowScriptAccess='always'></embed></object><br/><a href='http://www.5min.com/Video/Multiplying-Matrices-by-a-Scalar-161027697' style='font-family: Verdana;font-size: 10px;' target='_blank'>Multiplying matrices by a scalar</a></div> <p> </p> <style type="text/css">  </style> <p></p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p> </p>  <style type="text/css"> @import url(http://www.google.com/cse/api/branding.css); </style> <div class="cse-branding-right" style="background-color:#FFFFFF;color:#000000"> <div class="cse-branding-form"> <form action="http://www.onlinemathlearning.com/math-search.html" id="cse-search-box"> <div> <input type="hidden" name="cx" value="partner-pub-9460199170054827:r6p3zy-g6i5" /> <input type="hidden" name="cof" value="FORID:11" /> <input type="text" name="q" size="31" /> <input type="submit" name="sa" value="Search" /> </div> </form> </div> <div class="cse-branding-logo"> <img src="http://www.google.com/images/poweredby_transparent/poweredby_FFFFFF.gif" alt="Google" /> </div> <div class="cse-branding-text"> Custom Search </div> </div>  <p> </p> <span class="style2"><span class="style4">We welcome your feedback, comments and questions about this site - please submit your feedback via our <a href="http://www.onlinemathlearning.com/feedback.html">Feedback</a> page.</span></p> </span> <p> </p> <cite class="copyright"> © Copyright 2005, 2008 - onlinemathlearning.com <br>Embedded content, if any, are copyrights of their respective owners. </cite> <HR> <span class="footer-link">Useful Links:<a href="file:///C|/Documents%20and%20Settings/Jonathan/My%20Documents/JinAi/math/OML-Gmat/www.mba.com" target="_blank">mba.com</a><BR> <p> </p> </TD> </TR> </TBODY> </TABLE> </TD> <TD vAlign=top width=305> <p> </p>  <style type="text/css"> @import url(http://www.google.com/cse/api/branding.css); </style> <div class="cse-branding-bottom" style="background-color:#FFFFFF;color:#000000"> <div class="cse-branding-form"> <form action="http://www.onlinemathlearning.com/math-search.html" id="cse-search-box"> <div> <input type="hidden" name="cx" value="partner-pub-9460199170054827:r6p3zy-g6i5" /> <input type="hidden" name="cof" value="FORID:11" /> <input type="text" name="q" size="31" /> <input type="submit" name="sa" value="Search" /> </div> </form> </div> <div class="cse-branding-logo"> <img src="http://www.google.com/images/poweredby_transparent/poweredby_FFFFFF.gif" alt="Google" /> </div> <div class="cse-branding-text"> Custom Search </div> </div>  <p></p> <script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p></p> <TABLE cellSpacing=2 cellPadding=5 width=190 align=left border=0> <TR> <TD><SCRIPT charset="utf-8" type="text/javascript" src="http://ws.amazon.com/widgets/q?ServiceVersion=20070822&MarketPlace=US&ID=V20070822/US/onlinemathlea-20/8002/1f15b062-743e-4ced-8ff7-cf2b70aa65fe"> </SCRIPT> <NOSCRIPT><A HREF="http://ws.amazon.com/widgets/q?ServiceVersion=20070822&MarketPlace=US&ID=V20070822%2FUS%2Fonlinemathlea-20%2F8002%2F1f15b062-743e-4ced-8ff7-cf2b70aa65fe&Operation=NoScript" onClick="window.location.href='http://www.onlinemathlearning.com/cgi-bin/counter.pl?url=http%3A%2F%2Fws%2Eamazon%2Ecom%2Fwidgets%2Fq%3FServiceVersion%3D20070822%26MarketPlace%3DUS%26ID%3DV20070822%252FUS%252Fonlinemathlea-20%252F8002%252F1f15b062-743e-4ced-8ff7-cf2b70aa65fe%26Operation%3DNoScript&referrer=http%3A%2F%2Fwww%2Eonlinemathlearning%2Ecom%2Fmatrix-scalar-multiplication%2Ehtml'; return false;">Amazon.com Widgets</A></NOSCRIPT> </TD> </TR> </TABLE> </TD> </TR> </TBODY> </TABLE> </BODY> </HTML>

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grades 7 and 8

Grade 9