What is the size of the resulting product matrix AB if A € M9x5 and B € M5x14 ? AB has rows and columns.
What is the size of the resulting product matrix AB if A € M9x5 and B € M5x14 ? AB has rows and columns.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Matrix Multiplication Dimensions Problem**
**Problem Statement:**
What is the size of the resulting product matrix \( AB \) if \( A \in M_{9 \times 5} \) and \( B \in M_{5 \times 14} \)?
**Question:**
\( AB \) has [ ] rows and [ ] columns.
**Explanation:**
When multiplying two matrices \( A \) and \( B \), the product \( AB \) is defined if the number of columns of \( A \) is equal to the number of rows of \( B \). The resulting matrix \( AB \) will have the same number of rows as \( A \) and the same number of columns as \( B \). Therefore, for matrices \( A \in M_{9 \times 5} \) and \( B \in M_{5 \times 14} \), the product matrix \( AB \) has 9 rows and 14 columns.
### Final Answer:
- \( AB \) has 9 rows and 14 columns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2F2e1d3abc-7dd7-4964-82a8-52c44724159a%2F03ju2vo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplication Dimensions Problem**
**Problem Statement:**
What is the size of the resulting product matrix \( AB \) if \( A \in M_{9 \times 5} \) and \( B \in M_{5 \times 14} \)?
**Question:**
\( AB \) has [ ] rows and [ ] columns.
**Explanation:**
When multiplying two matrices \( A \) and \( B \), the product \( AB \) is defined if the number of columns of \( A \) is equal to the number of rows of \( B \). The resulting matrix \( AB \) will have the same number of rows as \( A \) and the same number of columns as \( B \). Therefore, for matrices \( A \in M_{9 \times 5} \) and \( B \in M_{5 \times 14} \), the product matrix \( AB \) has 9 rows and 14 columns.
### Final Answer:
- \( AB \) has 9 rows and 14 columns.
Expert Solution
Step 1: Matrix multiplication
We have to find the size of the matrix AB where size of A and B is given.
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