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Example 13 Les A-[³3] and [3] A= B= Find AB and BA if they exist.

Example 13 Les A-[³3] and [3] A= B= Find AB and BA if they exist.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 21EQ: Students frequently perform the following type of calculation to introduce a zero into a matrix:...
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MATRIX MULTIPLICATION - THE PRODUCT OF TWO MATRICES Conditions for matrix multiplication: Example 13 order of 1st matrix mxn + Let A ( 3 ) and B-[3] B= Example 14 Let A = AB BA AC CA CD DC For matrix multiplication to be defined: BE ED Are the following matrix products defined? What will the order of the product matrix be? Matrix product defined undefined order DE order must be the same The order of the "answer" matrix is mx p Find AB and BA if they exist. 2nd matrix nx p =[35₂] = [₂] = [2²], D = [12 -3], E = - A 8 | Page
Transcribed Image Text:MATRIX MULTIPLICATION - THE PRODUCT OF TWO MATRICES Conditions for matrix multiplication: Example 13 order of 1st matrix mxn + Let A ( 3 ) and B-[3] B= Example 14 Let A = AB BA AC CA CD DC For matrix multiplication to be defined: BE ED Are the following matrix products defined? What will the order of the product matrix be? Matrix product defined undefined order DE order must be the same The order of the "answer" matrix is mx p Find AB and BA if they exist. 2nd matrix nx p =[35₂] = [₂] = [2²], D = [12 -3], E = - A 8 | Page
How to multiply Matrices: Multiplying is a very tedious and error prone process. We will learn how to do it by hand, however we will mostly use the calculator to multiply matrices for us. Row 1 in the first matrix multiplies Column 1 in the second. The elements are multiplied in pairs and then added together. Then Row 1 in the first matrix multiplies Column 2 in the second. The result goes in position row 1, col 2 in the product matrix. Each row in the first matrix multiplies each column in the second. 2 L3 1 2 I: 5L4 0 [-530-3] Example 15 Multiply by hand and then check with calculator 5 6 -4 4 7 9 W N Y N 2 -7 2 5. -3 9| Page
Transcribed Image Text:How to multiply Matrices: Multiplying is a very tedious and error prone process. We will learn how to do it by hand, however we will mostly use the calculator to multiply matrices for us. Row 1 in the first matrix multiplies Column 1 in the second. The elements are multiplied in pairs and then added together. Then Row 1 in the first matrix multiplies Column 2 in the second. The result goes in position row 1, col 2 in the product matrix. Each row in the first matrix multiplies each column in the second. 2 L3 1 2 I: 5L4 0 [-530-3] Example 15 Multiply by hand and then check with calculator 5 6 -4 4 7 9 W N Y N 2 -7 2 5. -3 9| Page
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