Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. {x+3y+4z=−3x+2y+3z=−2x+4y+3z=−6\begin{cases} x + 3y + 4z = -3 \\ x + 2y + 3z = -2 \\ x + 4y + 3z = -6 \end{cases}⎩⎨⎧x+3y+4z=−3x+2y+3z=−2x+4y+3z=−6

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 31

7장, 문제 31

Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.
$\begin{cases}\)x + 3y + 4z = -3 $\x$ + 2y + 3z = -2 $\x$ + 4y + 3z = -6\(\end{cases}$

검증된 단계별 안내

Identify the variables and write them as a column matrix $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$.

Extract the coefficients of the variables from each equation to form the coefficient matrix $A = \begin{bmatrix} 1 & 3 & 4 \\ 1 & 2 & 3 \\ 1 & 4 & 3 \end{bmatrix}$.

Write the constants from the right side of each equation as the constant matrix $B = \begin{bmatrix} -3 \\ -2 \\ -6 \end{bmatrix}$.

Express the system of equations in the matrix form $AX = B$, where $A$ is the coefficient matrix, $X$ is the variable matrix, and $B$ is the constant matrix.

The final matrix equation is $\begin{bmatrix} 1 & 3 & 4 \\ 1 & 2 & 3 \\ 1 & 4 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -3 \\ -2 \\ -6 \end{bmatrix}$.

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.

Systems of Linear Equations

A system of linear equations consists of multiple linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. Understanding how to represent and solve these systems is fundamental in algebra.

Matrix Representation of Linear Systems

A system of linear equations can be expressed in matrix form as AX = B, where A is the coefficient matrix containing the coefficients of variables, X is the column matrix of variables, and B is the constant matrix. This form simplifies solving and analyzing the system.

Coefficient and Constant Matrices

The coefficient matrix (A) includes all coefficients of the variables arranged by equation and variable order, while the constant matrix (B) contains the constants from the right side of each equation. Correctly identifying these matrices is essential for forming the matrix equation.