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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 17
7장, 문제 17

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. X - A = B

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Identify the given matrices: \( A = \begin{bmatrix} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{bmatrix} \) and \( B = \begin{bmatrix} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{bmatrix} \). The equation to solve is \( X - A = B \).
To isolate \( X \), add matrix \( A \) to both sides of the equation: \( X - A + A = B + A \), which simplifies to \( X = B + A \).
Perform matrix addition by adding corresponding elements of matrices \( B \) and \( A \). For example, the element in the first row and first column of \( X \) is \( B_{11} + A_{11} = -5 + (-3) \).
Continue adding each corresponding element: \( X_{12} = B_{12} + A_{12} = -1 + (-7) \), \( X_{21} = B_{21} + A_{21} = 0 + 2 \), and so on for all elements.
Write the resulting matrix \( X \) after completing the addition of all corresponding elements from \( A \) and \( B \).

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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. To subtract matrix A from matrix X, each element in A is subtracted from the corresponding element in X. This operation is essential for solving equations like X - A = B.
추천 영상:
03:18
Adding and Subtracting Complex Numbers

Solving Matrix Equations

To solve matrix equations such as X - A = B, isolate the unknown matrix X by performing inverse operations. Here, adding matrix A to both sides yields X = B + A. Understanding how to manipulate matrices algebraically is crucial for finding the solution.
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Solving Logarithmic Equations

Matrix Dimensions and Compatibility

Matrix operations require that matrices have compatible dimensions. Both A and B must be the same size to perform addition or subtraction. Recognizing the dimensions ensures valid operations and helps avoid errors when solving matrix equations.
추천 영상:
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Introduction to Matrices
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