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If a matrix A is 9x3 and the product AB is 9x8, what is the size of B? The size of B isx0.

If a matrix A is 9x3 and the product AB is 9x8, what is the size of B? The size of B isx0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Matrix Size Problem** Given: - Matrix A is of size \(9 \times 3\). - The product matrix \(AB\) is of size \(9 \times 8\). **Task:** Determine the size of matrix B. **Solution:** To find the size of matrix B, consider the following matrix multiplication rule: - If matrix A is of size \(m \times n\) and matrix B is of size \(n \times p\), then the product matrix \(AB\) will be of size \(m \times p\). From the given information: - Matrix A is \(9 \times 3\). - Matrix \(AB\) is \(9 \times 8\). Since the number of columns in matrix A (3) must match the number of rows in matrix B, matrix B will be of size \(3 \times 8\). **Final Answer:** - The size of B is \(3 \times 8\).
Transcribed Image Text:**Matrix Size Problem** Given: - Matrix A is of size \(9 \times 3\). - The product matrix \(AB\) is of size \(9 \times 8\). **Task:** Determine the size of matrix B. **Solution:** To find the size of matrix B, consider the following matrix multiplication rule: - If matrix A is of size \(m \times n\) and matrix B is of size \(n \times p\), then the product matrix \(AB\) will be of size \(m \times p\). From the given information: - Matrix A is \(9 \times 3\). - Matrix \(AB\) is \(9 \times 8\). Since the number of columns in matrix A (3) must match the number of rows in matrix B, matrix B will be of size \(3 \times 8\). **Final Answer:** - The size of B is \(3 \times 8\).
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