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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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