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

Hello, everyone. We are asked to apply the given operation on the following matrices. We are given a two by three matrix where the first row reads 715, 2nd row reads 36 11. We are asked to subtract a two by two matrix where the top row reads 94. And the second row is 83, we have four answer choices. Two of them are two by three matrices. One is a two by two matrix and one says this is not possible. Recall that to add or subtract matrices, we must have the same dimensions between both matrices. Our first matrix has two rows and three columns. So it's a two by three matrix. Our second matrix has two rows and two columns. It is a two by two matrix. These do not match. So this means that this operation is not possible. It's answer choice. D not possible. Have a nice day.

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

College Algebra

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

1:21 minutes

Problem 75

Textbook Question

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

Verified step by step guidance

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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Key Concepts

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

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.

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