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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblem 11a
Chapter 7, Problem 11a

In Exercises 9 - 16, find the following matrices: a. A + B
Matrices A and B for exercise 11 in college algebra, chapter on matrices and determinants.

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Step 1: Understand that to add two matrices, they must have the same dimensions. Here, matrix A and matrix B are both 3x2 matrices, so addition is possible.
Step 2: Write down the matrices explicitly: A = \(\begin{bmatrix}\) 1 & 3 \\ 3 & 4 \\ 5 & 6 \(\end{bmatrix}\), B = \(\begin{bmatrix}\) 2 & -1 \\ 3 & -2 \\ 0 & 1 \(\end{bmatrix}\)
Step 3: Add the corresponding elements of matrices A and B. This means adding each 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 all elements.
Step 4: Express the sum matrix C = A + B as: C = \(\begin{bmatrix}\) 1+2 & 3+(-1) \\ 3+3 & 4+(-2) \\ 5+0 & 6+1 \(\end{bmatrix}\)
Step 5: Simplify each element in the resulting matrix to get the final matrix sum (do not calculate the final values here, just set up the expression).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. This operation is only defined when both matrices have the same number of rows and columns.
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Matrix Dimensions

The dimension of a matrix is given by the number of rows and columns it contains, expressed as 'rows × columns'. For matrix addition to be valid, both matrices must have identical dimensions, ensuring each element has a corresponding element to add.
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Element-wise Operations

Element-wise operations on matrices, such as addition, require performing the operation on each pair of corresponding elements individually. Understanding this concept helps in correctly computing the sum of matrices by focusing on each element's position.
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Related Practice
Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. {x+y=7x−y=3\(\begin{cases}\)x + y = 7 \(\x\) - y = 3\(\end{cases}\)

Textbook Question

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A=[00−21−101101−10100−1],B=[1203011101011202]A = \(\begin{bmatrix}\) 0 & 0 & -2 & 1 \\ -1 & 0 & 1 & 1 \\ 0 & 1 & -1 & 0 \\ 1 & 0 & 0 & -1 \(\end{bmatrix}\), \(\quad\) B = \(\begin{bmatrix}\) 1 & 2 & 0 & 3 \\ 0 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 1 & 2 & 0 & 2 \(\end{bmatrix}\)

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A

Textbook Question

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

[1141∣3−11−10∣72005∣1100124∣5]\(\begin{bmatrix}\)1 & 1 & 4 & 1 & \(\vert\) & 3 \\-1 & 1 & -1 & 0 & \(\vert\) & 7 \\2 & 0 & 0 & 5 & \(\vert\) & 11 \\0 & 0 & 12 & 4 & \(\vert\) & 5\(\end{bmatrix}\)

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Textbook Question

In Exercises 9 - 16, find the following matrices: b. A - B

Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B