Math Problem Statement

Find the value in row 2 column 1 of A + B, where A and B are given matrices.

Solution

Let's solve the given problem!

The task is to calculate the value in row 2, column 1 of the matrix A+BA + B, where:

1 & 3 & 5 \\ 5 & -1 & 1 \\ 3 & 0 & -2 \end{bmatrix}, \quad B = \begin{bmatrix} 3 & -5 & 2 \\ 3 & 4 & 0 \\ 2 & 1 & -3 \end{bmatrix}.$$ ### Step 1: Add the corresponding elements of matrices $$A$$ and $$B$$. Matrix addition involves adding corresponding elements. For row 2, column 1: $$(A + B)_{2,1} = A_{2,1} + B_{2,1}.$$ From $$A$$, $$A_{2,1} = 5$$. From $$B$$, $$B_{2,1} = 3$$. $$(A + B)_{2,1} = 5 + 3 = 8.$$ ### Final Answer: The value in row 2, column 1 of $$A + B$$ is **8**. Let me know if you'd like further clarification or more detailed steps! --- #### Related Questions: 1. How do you perform matrix addition in general? 2. What is the resulting full matrix $$A + B$$? 3. What are the properties of matrix addition? 4. How does matrix addition differ from matrix multiplication? 5. How would this problem change if it asked for $$A - B$$ instead of $$A + B$$? --- #### Tip: When adding or subtracting matrices, always ensure they have the same dimensions.

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Math Problem Analysis

Mathematical Concepts

Matrix Addition
Linear Algebra

Formulas

(A + B)_{ij} = A_{ij} + B_{ij}

Theorems

Properties of Matrix Addition

Suitable Grade Level

Grades 9-12