Skip to main content
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 23
7장, 문제 23

Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. B - X = 4A

검증된 단계별 안내
1
Start with the given matrix equation: \(B - X = 4A\).
To isolate \(X\), subtract \(B\) from both sides and multiply by \(-1\): \(X = B - 4A\).
Calculate \$4A\( by multiplying each element of matrix \)A$ by 4: \(4A = 4 \times \begin{bmatrix} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{bmatrix}\).
Perform the matrix subtraction \(B - 4A\) by subtracting corresponding elements of \$4A\( from \)B$: \(X = \begin{bmatrix} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{bmatrix} - 4A\).
Write the resulting matrix \(X\) with the calculated values from the subtraction.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m
도움이 되었나요?

주요 개념

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

Matrix Addition and Subtraction

Matrix addition and subtraction involve combining corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is found by adding or subtracting the elements in the same position from the original matrices. This operation is fundamental for solving equations involving matrices.
추천 영상:
03:18
Adding and Subtracting Complex Numbers

Scalar Multiplication of Matrices

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). This operation scales the matrix and is essential when manipulating matrix equations, such as multiplying matrix A by 4 in the given problem.
추천 영상:
4:35
Introduction to Matrices

Solving Matrix Equations

Solving matrix equations requires isolating the unknown matrix by performing inverse operations, similar to algebraic equations. For the equation B - X = 4A, you can isolate X by subtracting 4A from B or rearranging terms, ensuring all operations respect matrix dimensions.
추천 영상:
5:02
Solving Logarithmic Equations
관련 실천
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+2x+3y−z=72x−3y+z=4w−4x+y=3\(\begin{cases}\) w + 2x + 3y - z = 7 \\ 2x - 3y + z = 4 \\ w - 4x + y = 3 \(\end{cases}\)

672
views
교과서 질문

Let A=[−3−72−950]A = \(\begin{bmatrix}\) -3 & -7 \\ 2 & -9 \\ 5 & 0 \(\end{bmatrix}\) and B=[−5−1003−4]B = \(\begin{bmatrix}\) -5 & -1 \\ 0 & 0 \\ 3 & -4 \(\end{bmatrix}\). Solve each matrix equation for X. 4A + 3B = - 2X

77
views
교과서 질문

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

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\(\end{bmatrix}\)

966
views
교과서 질문

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{2x−y−z=4x+y−5z=−4x−2y=4\(\begin{cases}\) 2x - y - z = 4 \\ x + y - 5z = -4 \\ x - 2y = 4 \(\end{cases}\)

1039
views
교과서 질문

In Exercises 23–30, use expansion by minors to evaluate each determinant. ∣310−340−13−5∣\(\begin{vmatrix}\) 3 & 1 & 0 \\ -3 & 4 & 0 \\ -1 & 3 & -5 \(\end{vmatrix}\)

728
views
교과서 질문

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{x+3y=0x+y+z=13x−y−z=11\(\begin{cases}\) x + 3y = 0 \\ x + y + z = 1 \\ 3x - y - z = 11 \(\end{cases}\)

1015
views