MATLAB - Linear Algebra
Given A = [1 2; 3 4] and C = [5 6; 7 8], what is the result of inv(A*C)?
Given A = [1 2; 3 4] and C = [5 6; 7 8], what is the result of inv(A*C)?
hard📝 Application Q9 of 15
Step-by-Step Solution
Solution:
Step 1: Recall inverse of product property
For invertible matrices A and C, inv(A*C) = inv(C)*inv(A).Step 2: Check invertibility
Both A and C are square and invertible (determinants non-zero), so property applies.Final Answer:
inv(C)*inv(A) -> Option BQuick Check:
inv(A*C) = inv(C)*inv(A) [OK]
Quick Trick: Inverse of product reverses order: inv(AB) = inv(B)inv(A) [OK]
Common Mistakes:
- Assuming inv(A*C) = inv(A)*inv(C)
- Adding inverses instead of multiplying
- Ignoring matrix invertibility
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