I'll solve each problem step by step, checking the dimensions of matrices A and B to determine if multiplication AB can be performed.
Key Rule: Matrix multiplication AB is possible when the number of columns in A equals the number of rows in B.
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## Problem 1:
Matrix A = [3 × 2] (3 rows, 2 columns)
Matrix B = [2 × 6] (2 rows, 6 columns)
Check: Does columns of A (2) = rows of B (2)?
Yes, 2 = 2 ✓
Answer:
Yes
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## Problem 2:
Matrix A = [4 × 5] (4 rows, 5 columns)
Matrix B = [5 × 4] (5 rows, 4 columns)
Check: Does columns of A (5) = rows of B (5)?
Yes, 5 = 5 ✓
Answer:
Yes
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## Problem 3:
Matrix A = [5 × 2] (5 rows, 2 columns)
Matrix B = [2 × 4] (2 rows, 4 columns)
Check: Does columns of A (2) = rows of B (2)?
Yes, 2 = 2 ✓
Answer:
Yes
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## Problem 4:
Matrix A = [5 × 5] (5 rows, 5 columns)
Matrix B = [3 × 5] (3 rows, 5 columns)
Check: Does columns of A (5) = rows of B (3)?
No, 5 ≠ 3 ✗
Answer:
No
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Final Answer:
1. Yes
2. Yes
3. Yes
4. No
Parent Tip: Review the logic above to help your child master the concept of multiplying matrices worksheet with answers.
