Matrix Multiplication Conditions

00:00 3 marks

Given two matrices A (of size \(m \times n\)) and B (of size \(p \times q\)), state the condition that must be satisfied for the product \(AB\) to be defined. Briefly explain why this condition is necessary.

Hint Hint

Hint

Recall that the number of columns in matrix A must equal the number of rows in matrix B.

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The product \(AB\) is defined only if \(n = p\) because the inner dimensions of the two matrices must match to compute the dot product for each entry in the resulting matrix.

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Matrix Multiplication Conditions

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Matrix Multiplication Conditions

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