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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 14c
7장, 문제 14c

In Exercises 9 - 16, find the following matrices: c. - 4A
Matrices A and B for exercise 14 in college algebra, chapter 7 on systems of equations.

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1
Identify the matrix A given as [6 2 -3].
Understand that the problem asks to find the matrix resulting from multiplying matrix A by the scalar -4, which means each element of A will be multiplied by -4.
Multiply each element of matrix A by -4: multiply 6 by -4, 2 by -4, and -3 by -4 separately.
Write the resulting matrix after scalar multiplication as [-24 -8 12] (do not calculate the final values here, just show the multiplication step).
Confirm that the resulting matrix has the same dimensions as matrix A, but with each element scaled by -4.

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주요 개념

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

Matrix Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). For example, multiplying matrix A by -4 means each entry in A is multiplied by -4, resulting in a new matrix with scaled values.
추천 영상:
03:42
Finding Zeros & Their Multiplicity

Matrix Notation and Elements

A matrix is a rectangular array of numbers arranged in rows and columns. Understanding the notation, such as A = [6 2 -3], helps identify individual elements to perform operations like addition, subtraction, or scalar multiplication.
추천 영상:
05:18
Interval Notation

Basic Matrix Operations

Basic operations on matrices include addition, subtraction, and scalar multiplication. These operations follow specific rules, such as element-wise addition or multiplying each element by a scalar, which are foundational for solving systems of equations and other algebraic problems.
추천 영상:
8:38
Performing Row Operations on Matrices
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교과서 질문

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

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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=[3−1−42]A = \(\begin{bmatrix}\) 3 & -1 \\ -4 & 2 \(\end{bmatrix}\)

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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. {2x+y−z=23x+3y−2z=3\(\begin{cases}\) 2x + y - z = 2 \\ 3x + 3y - 2z = 3 \(\end{cases}\)

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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: a. A + B

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