Let A=[ a11 a12 a21 a22 ], B=[ b11 b12 b21 b22 ], and C=[ c11

Name: Problem 83, Chapter 9: Precalculus Functions and Graphs
Uploaded: 2020-09-15T18:01:47-08:00
Duration: 2 min 41 s
Channel: Derrick Hanson
Description: Let A=[ a11 a12 a21 a22 ], B=[ b11 b12 b21 b22 ], and C=[ c11 c12 c21 c22 ] Determine whether each of the following statements is true, and explain your answer. A B=B A (commutative)

step 1 we are asked whether we think the commutative property holds true for matrices. In this case, me

Question

Let $A=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right], B=\left[\begin{array}{ll}b_{11} & b_{12} \\ b_{21} & b_{22}\end{array}\right],$ and $C=\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]$ Determine whether each of the following statements is true, and explain your answer. $A B=B A$ (commutative)

   Let $A=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right], B=\left[\begin{array}{ll}b_{11} & b_{12} \\ b_{21} & b_{22}\end{array}\right],$ and $C=\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]$
Determine whether each of the following statements is true, and explain your answer.
$A B=B A$ (commutative)

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 9, Problem 83

Instant Answer

Solved by Expert Derrick Hanson

09/15/2020

Step 1

The multiplication of two matrices is done by taking the rows of the first matrix and the columns of the second matrix. The element in the $i$-th row and $j$-th column of the product matrix is the sum of the product of corresponding elements from the $i$-th row of Show more…

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Let $A=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right], B=\left[\begin{array}{ll}b_{11} & b_{12} \\ b_{21} & b_{22}\end{array}\right],$ and $C=\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]$ Determine whether each of the following statements is true, and explain your answer. $A B=B A$ (commutative)

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Key Concepts

Matrix Multiplication

Matrix multiplication is an operation that involves taking the dot product of rows from the first matrix with columns of the second matrix. The procedure inherently depends on the order of the matrices, meaning the first matrix determines the row choices and the second determines the column selections.

Non-Commutativity

In general, matrix multiplication is non-commutative. This means that for most matrices, the product AB will not equal BA. Commutativity holds only under special circumstances, such as when the matrices possess particular structures or relationships that cause the order to be irrelevant.

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