Problem

Given two matrices: A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]. Find the result of A + B.

Answer

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Answer

\[ [A + B]_22 = A_22 + B_22 = 4 + 8 = 12 \]

Steps

Step 1 ：First, recall the rule for matrix addition. Two matrices can be added if and only if they have the same dimensions. The sum of two matrices A and B is obtained by adding corresponding elements: (A + B)_{ij} = A_{ij} + B_{ij}.

Step 2 ：Applying this rule to the given matrices, we get: \[ [A + B]_11 = A_11 + B_11 = 1 + 5 = 6 \]

Step 3 ：\[ [A + B]_12 = A_12 + B_12 = 2 + 6 = 8 \]

Step 4 ：\[ [A + B]_21 = A_21 + B_21 = 3 + 7 = 10 \]

Step 5 ：\[ [A + B]_22 = A_22 + B_22 = 4 + 8 = 12 \]

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