For the given matrices A and B find each of the following. (a) A+B (b) B+A (c) A-B A=[ 3

Name: Problem 13, Chapter 6: College Algebra with Modeling and Visualization
Uploaded: 2021-06-27T20:42:24-08:00
Duration: 1 min 37 s
Channel: Kyle Christian
Description: For the given matrices A and B find each of the following. (a) A+B (b) B+A (c) A-B A=[ 3 4 -1 0 -3 2 -2 5 10 ] B=[ 11 5 -2 4 -7 12 6 6 6 ]

step 1 All right, for this problem, we're taking these matrices A and B. We're going to add or subtract

Question

For the given matrices $A$ and $B$ find each of the following. (a) $\boldsymbol{A}+\boldsymbol{B} \quad$ (b) $\boldsymbol{B}+\boldsymbol{A} \quad(\boldsymbol{c}) \boldsymbol{A}-\boldsymbol{B}$ $$A=\left[\begin{array}{rrr}3 & 4 & -1 \\0 & -3 & 2 \\-2 & 5 & 10\end{array}\right]$$ $$B=\left[\begin{array}{rrr}11 & 5 & -2 \\4 & -7 & 12 \\6 & 6 & 6\end{array}\right]$$

   For the given matrices $A$ and $B$ find each of the following.
(a) $\boldsymbol{A}+\boldsymbol{B} \quad$ (b) $\boldsymbol{B}+\boldsymbol{A} \quad(\boldsymbol{c}) \boldsymbol{A}-\boldsymbol{B}$
$$A=\left[\begin{array}{rrr}3 & 4 & -1 \\0 & -3 & 2 \\-2 & 5 & 10\end{array}\right]$$
$$B=\left[\begin{array}{rrr}11 & 5 & -2 \\4 & -7 & 12 \\6 & 6 & 6\end{array}\right]$$

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 6, Problem 13

Instant Answer

Solved by Expert Kyle Christian

06/27/2021

Step 1

This means we add the element in the first row and first column of A to the element in the first row and first column of B, and so on for each element in the matrices. Show more…

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For the given matrices $A$ and $B$ find each of the following. (a) $\boldsymbol{A}+\boldsymbol{B} \quad$ (b) $\boldsymbol{B}+\boldsymbol{A} \quad(\boldsymbol{c}) \boldsymbol{A}-\boldsymbol{B}$ $$A=\left[\begin{array}{rrr}3 & 4 & -1 \\0 & -3 & 2 \\-2 & 5 & 10\end{array}\right]$$ $$B=\left[\begin{array}{rrr}11 & 5 & -2 \\4 & -7 & 12 \\6 & 6 & 6\end{array}\right]$$

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Key Concepts

Matrix Addition

Matrix addition is the process of adding two matrices by summing the elements that occupy the same positions in each matrix. This operation requires that the matrices involved share the same dimensions, and it is performed element-wise.

Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices that have the same dimensions. This operation essentially subtracts each entry of one matrix from the corresponding entry of the other matrix, similar to element-wise addition but with subtraction instead.

Commutative Property of Addition

The commutative property of matrix addition states that changing the order in which two matrices are added does not affect the result; that is, A + B is equal to B + A. This property is fundamental to the structure of matrices under addition.

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