Matrix Addition and Subtraction: Does Not Exist (DNE) Due to Dimension Mismatch

Math Problem Statement

Perform the indicated matrix operation. (If an answer does not exist, enter DNE.)

1 2

4 5

2 3 +

3 0 5

0 9

7 2 −6 2

To perform the matrix operation, we'll break it down into two parts: matrix addition and matrix subtraction.

We are given two matrices and a third matrix to subtract:

1 & 2 \\ 4 & 5 \\ 2 & 3 \end{bmatrix}$$ 2. Second matrix: $$\begin{bmatrix} 3 & 0 & 5 \\ 0 & 9 \\ 7 & 2 \end{bmatrix}$$ 3. Subtract matrix: $$\begin{bmatrix} -6 & 2 \end{bmatrix}$$ ### Step 1: Check matrix dimensions - The first matrix is a $$3 \times 2$$ matrix. - The second matrix is a $$3 \times 3$$ matrix. - The third matrix is a $$1 \times 2$$ matrix (row vector). Matrix addition and subtraction are only defined for matrices of the same dimension. Since the matrices have different dimensions (the second matrix is a $$3 \times 3$$ and others aren't), the matrix operation cannot be performed. ### Final Answer: $$\text{DNE (Does Not Exist)}$$ Would you like any additional details on matrix operations? Here are some related questions: 1. What are the rules for adding and subtracting matrices? 2. How do you multiply matrices with different dimensions? 3. Can you explain matrix scalar multiplication? 4. What are some examples of matrix operations used in physics? 5. How is matrix inversion calculated? **Tip:** Always check the dimensions of matrices before performing any operations like addition or subtraction!

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Matrix Operations
Matrix Addition
Matrix Subtraction
Matrix Dimensions

Matrix addition: A + B is defined if both A and B have the same dimensions.
Matrix subtraction follows the same rule as matrix addition.

Matrix Addition/Subtraction Theorem: Addition or subtraction of matrices is only possible when the dimensions of the matrices are the same.

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