In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. [x2yz9]=[41239]\begin{bmatrix} x & 2y \\ z & 9 \end{bmatrix} = \begin{bmatrix} 4 & 12 \\ 3 & 9 \end{bmatrix}[xz2y9]=[43129]

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 7

7장, 문제 7

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. $\begin{bmatrix}\) x & 2y \\ z & 9 $\end{bmatrix}$ = $\begin{bmatrix}$ 4 & 12 \\ 3 & 9 \(\end{bmatrix}$

검증된 단계별 안내

Understand that two matrices are equal if and only if their corresponding entries are equal.

Set up equations by equating each corresponding element from the two matrices: $x = 4$, $2y = 12$, $z = 3$, and $9 = 9$.

Solve the equation $2y = 12$ by dividing both sides by 2 to find the value of $y$.

Use the values found for $x$, $y$, and $z$ as the solution to the problem.

Verify your solution by substituting the values back into the original matrices to ensure both matrices are equal.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Matrix Equality

Two matrices are equal if and only if they have the same dimensions and their corresponding entries are equal. This means each element in one matrix must match the element in the same position in the other matrix.

Solving Systems of Equations

When matrices are equal, equate corresponding elements to form equations. Solving these equations simultaneously helps find the values of variables involved, such as x, y, and z in this problem.

Substitution and Simplification

After setting up equations from matrix equality, use substitution or algebraic manipulation to isolate variables. Simplifying these equations step-by-step leads to the solution for each variable.

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. [x2yz9]=[41239]\(\begin{bmatrix}\) x & 2y \\ z & 9 \(\end{bmatrix}\) = \(\begin{bmatrix}\) 4 & 12 \\ 3 & 9 \(\end{bmatrix}\)[xz2y9]=[43129]

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Matrix Equality

Solving Systems of Equations

Substitution and Simplification

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. $\begin{bmatrix}\) x & 2y \\ z & 9 \(\end{bmatrix}\) = \(\begin{bmatrix}\) 4 & 12 \\ 3 & 9 \(\end{bmatrix}$