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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 6 - Matrices and Determinants문제 13b
7장, 문제 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.

검증된 단계별 안내
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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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
추천 영상:
5:56
Adding & Subtracting Functions

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.
추천 영상:
4:35
Introduction to Matrices

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.
추천 영상:
8:38
Performing Row Operations on Matrices
관련 실천
교과서 질문

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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교과서 질문

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

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교과서 질문

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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교과서 질문

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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교과서 질문

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

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교과서 질문

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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