Find each sum or difference, if possible. [ 2 4 6 ] + [ − 2 − 4 − 6 ] \left[ \begin{matrix} 2 & 4 & 6 \end{matrix} \right] + \left[ \begin{matrix} -2 \\ -4 \\ -6 \end{matrix} \right]

Hello, everyone. We are asked to calculate the sum of the given matrices. If possible, we have a one by three matrix where the row reads 35 negative nine. And we're adding to that a three by one matrix where the column reads negative 281, we're given four answer choices three of which are matrices and one of which says the summ does not exist. Recall that in order to add or subtract matrices, we must have the same dimensions. In this example, we are given a one by three matrix and a three by one matrix. These are not the same dimensions. So they do not match, which means there is no solution to this. And the answer to D the sum does not exist is the correct answer. Have a nice day.

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Problem 29

Textbook Question

Find each sum or difference, if possible.
$[\begin{matrix} 2 & 4 & 6 \end{matrix}] + [\begin{matrix} - 2 \\ - 4 \\ - 6 \end{matrix}]$

Verified step by step guidance

Identify the dimensions of the matrices involved. A <3x1> matrix has 3 rows and 1 column, while a <1x3> matrix has 1 row and 3 columns.

Recall that matrix addition or subtraction is only defined when both matrices have the same dimensions (i.e., the same number of rows and columns).

Since the given matrices have different dimensions (<3x1> vs. <1x3>), they cannot be added or subtracted directly.

Therefore, conclude that the sum or difference of these two matrices is not possible due to incompatible dimensions.

If you want to perform operations involving these matrices, consider other operations like matrix multiplication, but addition and subtraction require matching dimensions.

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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, their sum or difference is undefined. Understanding this is crucial to determine if the operation is possible.

Matrix Addition and Subtraction

When two matrices have the same dimensions, their sum or difference is found by adding or subtracting corresponding elements. This operation is performed element-wise, resulting in a new matrix of the same size.

Matrix Notation and Representation

Matrices are represented by rows and columns, often denoted as m x n, where m is the number of rows and n is the number of columns. Recognizing the notation helps in visualizing the structure and performing operations correctly.

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