Find each sum or difference, if possible. [3−42−5−88]−[239−25−732]\left[ \begin{matrix} \sqrt{3} & -4 \\ 2 & -\sqrt{5} \\ -8 & \sqrt{8} \end{matrix} \right] - \left[ \begin{matrix} 2\sqrt{3} & 9 \\ -2 & \sqrt{5} \\ -7 & 3\sqrt{2} \end{matrix} \right]

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 37

6장, 문제 37

Find each sum or difference, if possible.
$[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]$

검증된 단계별 안내

Identify the dimensions of both matrices to ensure they are the same. Since both are 3x2 matrices, addition or subtraction is possible.

Recall that to add or subtract matrices, you perform the operation element-wise. This means subtracting corresponding elements from each matrix.

Label the elements of the first matrix as $a_{ij}$ and the second matrix as $b_{ij}$, where $i$ is the row number and $j$ is the column number.

Form the resulting matrix by calculating each element as $c_{ij} = a_{ij} - b_{ij}$ for all $i$ and $j$.

Write the resulting 3x2 matrix with the new elements $c_{ij}$, which represents the difference of the two matrices.

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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, their sum or difference is undefined. In this question, both matrices are 3x2, so they are compatible for addition or subtraction.

Matrix Addition and Subtraction

To add or subtract matrices, perform the operation element-wise by adding or subtracting corresponding entries from each matrix. For example, subtract the element in row 1, column 1 of the second matrix from the element in the same position of the first matrix, and repeat for all elements.

Representation and Notation of Matrices

A matrix is a rectangular array of numbers arranged in rows and columns, denoted by brackets. Understanding how to read and write matrices, including identifying elements by their row and column positions, is essential for performing operations like addition and subtraction.