Math Problem Statement

Evaluate the given expression. Take A =

0 −2

−2 0 1 1 and B =

−0.25 3

0 −0.25 −2 −1 . A + B

Solution

We are given two matrices AA and BB:

0 & -2 \\ -2 & 0 \\ 1 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} -0.25 & 3 \\ 0 & -0.25 \\ -2 & -1 \end{pmatrix}.$$ To compute $$A + B$$, we add the corresponding elements of the two matrices. $$A + B = \begin{pmatrix} 0 + (-0.25) & -2 + 3 \\ -2 + 0 & 0 + (-0.25) \\ 1 + (-2) & 1 + (-1) \end{pmatrix}$$ This simplifies to: $$A + B = \begin{pmatrix} -0.25 & 1 \\ -2 & -0.25 \\ -1 & 0 \end{pmatrix}$$ Thus, the sum $$A + B$$ is: $$A + B = \begin{pmatrix} -0.25 & 1 \\ -2 & -0.25 \\ -1 & 0 \end{pmatrix}.$$ Would you like further details or have any questions? Here are some related questions: 1. How do you subtract two matrices? 2. What is the transpose of a matrix? 3. How do you find the determinant of a matrix? 4. How do matrix multiplication rules differ from addition? 5. What is the inverse of a matrix? **Tip:** Matrix addition is only defined for matrices of the same dimensions; ensure that both matrices have matching sizes before adding.

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Matrix Addition

Formulas

A + B = [a_{ij} + b_{ij}]

Theorems

Matrix addition is only defined for matrices of the same dimensions

Suitable Grade Level

Grades 9-12