Find each sum or difference, if possible. [−43]−[582]\left[ \begin{matrix} -4 & 3 \end{matrix} \right] - \left[ \begin{matrix} 5 & 8 & 2 \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 35

6장, 문제 35

Find each sum or difference, if possible.
$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$

검증된 단계별 안내

Identify the dimensions of each matrix. The first matrix is a 1x2 matrix (1 row, 2 columns), and the second matrix is a 1x3 matrix (1 row, 3 columns).

Recall that matrix addition or subtraction is only possible when the two matrices have the same dimensions, meaning the same number of rows and columns.

Since the first matrix has 2 columns and the second matrix has 3 columns, their dimensions do not match.

Conclude that the subtraction of a 1x3 matrix from a 1x2 matrix is not defined because their sizes are different.

Therefore, the sum or difference cannot be performed in this case.

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주요 개념

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

Matrix Dimensions and Compatibility

Matrix addition and subtraction require the matrices to have the same dimensions, meaning the same number of rows and columns. If the matrices differ in size, such as a 1x2 matrix and a 1x3 matrix, their sum or difference is undefined because corresponding elements do not align.

Matrix Addition and Subtraction

To add or subtract matrices, you perform the operation element-wise, combining corresponding entries from each matrix. This process is only valid when both matrices share identical dimensions, ensuring each element has a matching counterpart.

Understanding Matrix Notation

A matrix is described by its dimensions, rows by columns (e.g., 1x2 means 1 row and 2 columns). Recognizing this notation helps determine if operations like addition or subtraction are possible and guides how to perform them correctly.

Find each sum or difference, if possible. [−43]−[582]\(\left\)[ \(\begin{matrix}\) -4 & 3 \(\end{matrix}\) \(\right\)] - \(\left\)[ \(\begin{matrix}\) 5 & 8 & 2 \(\end{matrix}\) \(\right\)]