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# Note for MATH 1313 with Professor Ahmed-Zaid at UH multiplication of matrices

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 79 views.

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Date Created: 02/06/15
as m acre Section 25 Multiplication of Matrices If A is a matrix of size mxn and B is a matrix of size nxp then the product AB is de ned and is a matrix of size mxp So two matrices can be multiplied if and only if the number of columns in the rst matrix is equal to the number of rows in the second matrix How to Multiply Two Matrices The element in the ith row and jth column of AB is found by multiplying each element in the ith row of A by the corresponding element in the jth column of B and adding the products Example 1 Your st ck holdings are given by the row matrix or vector GM IBM BAC A 700 400 200 At the clog of trading on a certain day the m in dollars per share of these stocks GM IBM BAC respectively are 50 B 120 42 What is the total value of your holdin as of that day do so mrwwm 160 be 1 39st 1E UL QO 3 9 3 l 4 l 3 0 710 9 6 1 Examp1e2 LetA B 2 0 3 C andD 2 4 71 76 4 0 9 1 2 1 8 4 X q f 3 W 2 am 3 0 2i Q 9 ll 14490 W 3 G0 Section 25 7 Multiplication ofMatrices l compute if possible39 b L in a 4 6 9 k W0 hmhkur if Hf 0 0x9 9 33 31 an La WW 4 3M 5 Lf2 S 5E1 1 I 33 10M Dd0a 3991006 in P l 4 I 3 Kquot 2 0 1 O S GUMSU oakL 1 g e 3 s 4JE J 7 quot3 El Ll LL 9 alLlfsz alluazs L2 9 H 4 LH39CW 2 41 Lawrqu l L 0 EA A E Q 2 Ll m a e o m W 2 4 4 L Q ngMJQZ gt 9 1 Note In general matrix multiplication is not commutative ithat is AB BA Section 25 7 Multiplication ofMatIices 2 71 fl 5 712 6 4 2 2 2 6 Example 3 Let A B andC 8 2 710 72 73 4 Find 05A CTB 1 Q q 1 wk ST ilk 1 1 l ll LgtHlo u Lt L g 6 lo M 1 g 63 q 7 M 9 M 1 A 25 3 1 q U39Q Wm TQ WM AJ ILW Section 25 7 Multiplication of Matiices EMHIZB gtQ1E 7 3 AWLmjQ N 1K9 JgMJSx 9 L 39H X 5 6 39S 5 l quot3 fl 1 5 Section 25 7 Multiplication of Matiices 4

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