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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 12b
Chapter 7, Problem 12b

In Exercises 9 - 16, find the following matrices: b. A - B
Matrices A and B for exercise 12 in college algebra, chapter on matrices and determinants.

Verified step by step guidance
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Step 1: Understand the problem. You are asked to find the matrix A - B, which means subtract matrix B from matrix A. Both matrices A and B are given as 2x3 matrices.
Step 2: Recall the rule for matrix subtraction. To subtract two matrices, subtract their corresponding elements. That is, if A = [a_ij] and B = [b_ij], then (A - B) = [a_ij - b_ij].
Step 3: Write down the matrices explicitly: A = \(\begin{bmatrix}\) 3 & 1 & 1 \\ -1 & 2 & 5 \(\end{bmatrix}\), B = \(\begin{bmatrix}\) 2 & -3 & 6 \\ -3 & 1 & -4 \(\end{bmatrix}\)
Step 4: Subtract each element of B from the corresponding element of A: - For the first row: (3 - 2), (1 - (-3)), (1 - 6) - For the second row: (-1 - (-3)), (2 - 1), (5 - (-4))
Step 5: Write the resulting matrix with the computed differences in each position to get A - B.

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Key Concepts

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

Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. Each element in the resulting matrix is found by subtracting the element in matrix B from the element in matrix A at the same position.
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Matrix Dimensions

For matrix operations like addition or subtraction to be valid, the matrices must have the same dimensions, meaning the same number of rows and columns. Here, both matrices A and B are 2x3 matrices, allowing element-wise subtraction.
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Element-wise Operations

Element-wise operations apply arithmetic operations to each corresponding element in matrices. In this problem, subtracting matrix B from matrix A means performing subtraction on each pair of elements located in the same row and column.
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Related Practice
Textbook Question

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

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Textbook Question

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

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Textbook Question

Use the fact that if A=[abcd]A = \(\begin{bmatrix}\) a & b \\ c & d \(\end{bmatrix}\), then A−1=1ad−bc[d−b−ca]A^{-1} = \(\frac{1}{ad-bc}\) \(\begin{bmatrix}\) d & -b \\ -c & a \(\end{bmatrix}\) to find the inverse of each matrix, if possible. Check that AA−1=I2AA^{-1} = I_2 and A−1A=I2A^{-1} A = I_2.

A=[23−12]A = \(\begin{bmatrix}\) 2 & 3 \\ -1 & 2 \(\end{bmatrix}\)

Textbook Question

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

Textbook Question

Find the following matrices: - 3A + 2B

A=[311−125],B=[2−36−31−4]A = \(\begin{bmatrix}\)3 & 1 & 1 \\-1 & 2 & 5\(\end{bmatrix}\), B = \(\begin{bmatrix}\)2 & -3 & 6 \\-3 & 1 & -4\(\end{bmatrix}\)

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Textbook Question

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