Write each matrix equation as a system of linear equations without matrices.[4−72−3][xy]=[−31]\begin{bmatrix} 4 & -7 \\ 2 & -3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -3 \\ 1 \end{bmatrix}[42−7−3][xy]=[−31]

Ch. 6 - Matrices and Determinants

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 33

7장, 문제 33

Write each matrix equation as a system of linear equations without matrices.
$\begin{bmatrix}\) 4 & -7 \\ 2 & -3 $\end{bmatrix}$ $\begin{bmatrix}$ x \\ y $\end{bmatrix}$ = $\begin{bmatrix}$ -3 \\ 1 \(\end{bmatrix}$

검증된 단계별 안내

Identify the given matrix equation: $\left[ \begin{array}{cc} 4 & -7 \\ 2 & -3 \end{array} \right] \left[ \begin{array}{c} x \\ y \end{array} \right] = \left[ \begin{array}{c} -3 \\ 1 \end{array} \right]$.

Recall that multiplying a matrix by a vector corresponds to forming linear combinations of the vector components with the matrix rows.

Write the first row multiplication as an equation: $4x - 7y = -3$.

Write the second row multiplication as an equation: $2x - 3y = 1$.

Thus, the matrix equation is equivalent to the system of linear equations: $\begin{cases} 4x - 7y = -3 \\ 2x - 3y = 1 \end{cases}$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Matrix Multiplication

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix and summing the products. In this problem, multiplying the 2x2 coefficient matrix by the 2x1 variable matrix results in a 2x1 matrix representing the system's left side.

System of Linear Equations

A system of linear equations consists of multiple linear equations with the same variables. Writing the matrix equation as a system means expressing each row multiplication as an individual linear equation involving variables x and y.

Equating Matrices to Form Equations

When two matrices are equal, their corresponding entries are equal. This principle allows us to set each element of the product matrix equal to the corresponding element in the constant matrix, forming a system of equations to solve.

Write each matrix equation as a system of linear equations without matrices.[4−72−3][xy]=[−31]\(\begin{bmatrix}\) 4 & -7 \\ 2 & -3 \(\end{bmatrix}\) \(\begin{bmatrix}\) x \\ y \(\end{bmatrix}\) = \(\begin{bmatrix}\) -3 \\ 1 \(\end{bmatrix}\)[42−7−3][xy]=[−31]

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Matrix Multiplication

System of Linear Equations

Equating Matrices to Form Equations

Write each matrix equation as a system of linear equations without matrices.
$\begin{bmatrix}\) 4 & -7 \\ 2 & -3 \(\end{bmatrix}\) \(\begin{bmatrix}\) x \\ y \(\end{bmatrix}\) = \(\begin{bmatrix}\) -3 \\ 1 \(\end{bmatrix}$