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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 13b
Chapter 7, Problem 13b

In Exercises 9 - 16, find the following matrices: b. A - B
Matrices A and B for exercise 13 in college algebra, showing their elements for subtraction.

Verified step by step guidance
1
Step 1: Understand the problem. You are asked to find the matrix A - B, where A and B are given matrices.
Step 2: Recall that matrix subtraction is performed by subtracting corresponding elements of the two matrices. That is, if A = [a_ij] and B = [b_ij], then A - B = [a_ij - b_ij].
Step 3: Write down the matrices A and B explicitly: A = \( \begin{bmatrix} 2 \\ -4 \\ 1 \end{bmatrix} \), B = \( \begin{bmatrix} -5 \\ 3 \\ -1 \end{bmatrix} \).
Step 4: Subtract each element of B from the corresponding element of A: For the first element, calculate 2 - (-5); for the second element, calculate -4 - 3; for the third element, calculate 1 - (-1).
Step 5: Write the resulting matrix with the new elements obtained from the subtraction in step 4.

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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. In this problem, both matrices A and B are 3x1 matrices, allowing subtraction.
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Element-wise Operations

Element-wise operations apply arithmetic operations to each corresponding element in matrices. Understanding this concept is essential to correctly perform matrix subtraction by handling each element individually.
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Related Practice
Textbook Question

Find the following matrices: A+BA + B

A=[2−41],B=[−53−1]A = \(\begin{bmatrix}\)2 \\-4 \\1\(\end{bmatrix}\), B = \(\begin{bmatrix}\)-5 \\3 \\-1\(\end{bmatrix}\)

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Textbook Question

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

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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 \(\end{bmatrix}\)

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Textbook Question

Perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

A=[2−1253−1]B=[0−2321−5]C=[123−112−121]D=[−2313−24]A=\(\begin{bmatrix}\)2 & -1 & 2\\ 5 & 3 & -1\(\end{bmatrix}\[\quad\) B=\(\begin{bmatrix}\)0 & -2\\ 3 & 2\\ 1 & -5\(\end{bmatrix}\)C=\(\begin{bmatrix}\)1 & 2 & 3\\ -1 & 1 & 2\\ -1 & 2 & 1\(\end{bmatrix}\]\quad\) D=\(\begin{bmatrix}\)-2 & 3 & 1\\ 3 & -2 & 4\(\end{bmatrix}\)

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Textbook Question

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

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Textbook Question

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. {w−3x+y−4z=4−2w+x+2y=−23w−2x+y−6z=2−w+3x+2y−z=−6\(\begin{cases}\)w - 3x + y - 4z = 4 \\-2w + x + 2y = -2 \\3w - 2x + y - 6z = 2 \\-w + 3x + 2y - z = -6\(\end{cases}\)

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