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

Hello, everyone. We are asked to calculate the difference for the given matrices. If possible, we are given a one by two matrix where the row reads negative 87. And we're subtracting a one by three matrix where the row reads 123, we have four answer choices three of which are matrices. And answer choice D says the difference does not exist. Recall that in order to add or subtract matrices, we need to have the same dimensions looking at the matrices here. Our first matrix is a one by two matrix and the second matrix is a one by three matrix. These do not have the same dimensions. They so they do not match in terms of dimensions. So this means that answer choice D is our solution. The difference does not exist have a nice day.

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Problem 35

Textbook Question

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

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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