Perform each operation, if possible. [258192]−[3471]\left[ \begin{matrix} 2 & 5 & 8 \\ 1 & 9 & 2 \end{matrix} \right] - \left[ \begin{matrix} 3 & 4 \\ 7 & 1 \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 75

6장, 문제 75

Perform each operation, if possible.
$[\begin{matrix} 2 & 5 & 8 \\ 1 & 9 & 2 \end{matrix}] - [\begin{matrix} 3 & 4 \\ 7 & 1 \end{matrix}]$

검증된 단계별 안내

Identify the dimensions of both matrices. The first matrix is a 3x2 matrix (3 rows and 2 columns), and the second matrix is a 2x2 matrix (2 rows and 2 columns).

Recall that matrix subtraction is only defined when both matrices have the same dimensions, meaning the same number of rows and columns.

Since the first matrix is 3x2 and the second is 2x2, their dimensions do not match.

Because the dimensions are different, the subtraction operation between these two matrices is not possible.

Therefore, you cannot perform the subtraction of a 3x2 matrix and a 2x2 matrix.

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주요 개념

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

Matrix Dimensions and Compatibility

Matrix operations like addition and subtraction require the matrices to have the same dimensions. This means the number of rows and columns in both matrices must be equal for the operation to be defined.

Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements from two matrices of the same size. Each element in the resulting matrix is found by subtracting the element in the second matrix from the element in the first matrix at the same position.

Understanding Matrix Notation

Matrix notation uses rows and columns to organize elements. A 3x2 matrix has 3 rows and 2 columns, while a 2x2 matrix has 2 rows and 2 columns. Recognizing these helps determine if operations like subtraction are possible.

Perform each operation, if possible. [258192]−[3471]\(\left\)[ \(\begin{matrix}\) 2 & 5 & 8 \\ 1 & 9 & 2 \(\end{matrix}\) \(\right\)] - \(\left\)[ \(\begin{matrix}\) 3 & 4 \\ 7 & 1 \(\end{matrix}\) \(\right\)]