Math Problem Statement
Given the matrices A=(-212011121) and B=(1-2111131-1) determine A+B (A-B)
Solution
We are tasked with calculating the sum and difference of two matrices and .
Given:
\begin{bmatrix} -2 & 1 & 2 \\ 0 & 1 & 1 \\ 1 & 2 & 1 \end{bmatrix} \quad B = \begin{bmatrix} 1 & -2 & 1 \\ 1 & 1 & 1 \\ 3 & 1 & -1 \end{bmatrix}$$ ### Matrix Addition: $$A + B$$ To add two matrices, add their corresponding elements: $$A + B = \begin{bmatrix} -2 + 1 & 1 + (-2) & 2 + 1 \\ 0 + 1 & 1 + 1 & 1 + 1 \\ 1 + 3 & 2 + 1 & 1 + (-1) \end{bmatrix}$$ Perform the operations: $$A + B = \begin{bmatrix} -1 & -1 & 3 \\ 1 & 2 & 2 \\ 4 & 3 & 0 \end{bmatrix}$$ ### Matrix Subtraction: $$A - B$$ To subtract two matrices, subtract their corresponding elements: $$A - B = \begin{bmatrix} -2 - 1 & 1 - (-2) & 2 - 1 \\ 0 - 1 & 1 - 1 & 1 - 1 \\ 1 - 3 & 2 - 1 & 1 - (-1) \end{bmatrix}$$ Perform the operations: $$A - B = \begin{bmatrix} -3 & 3 & 1 \\ -1 & 0 & 0 \\ -2 & 1 & 2 \end{bmatrix}$$ ### Final Results: $$A + B = \begin{bmatrix} -1 & -1 & 3 \\ 1 & 2 & 2 \\ 4 & 3 & 0 \end{bmatrix}$$ $$A - B = \begin{bmatrix} -3 & 3 & 1 \\ -1 & 0 & 0 \\ -2 & 1 & 2 \end{bmatrix}$$ --- Would you like a detailed explanation of these operations? #### Related Questions: 1. What are the properties of matrix addition and subtraction? 2. Can you calculate $$2A + 3B$$ for these matrices? 3. What happens if $$A = B$$ in matrix subtraction? 4. How do matrix operations change if the matrices are not the same size? 5. Can you verify the commutative property for addition using $$A + B$$? **Tip:** Always check the dimensions of matrices before performing operations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Operations
Matrix Addition
Matrix Subtraction
Formulas
Matrix Addition: (A + B)_{ij} = A_{ij} + B_{ij}
Matrix Subtraction: (A - B)_{ij} = A_{ij} - B_{ij}
Theorems
Matrix addition and subtraction require matrices to have the same dimensions.
Suitable Grade Level
Grades 9-12