MATLAB - Linear Algebra
You have a matrix A = [4 7; 2 6]. Write MATLAB code to compute its inverse and multiply it by B = [1; 0]. What is the resulting vector?
You have a matrix A = [4 7; 2 6]. Write MATLAB code to compute its inverse and multiply it by B = [1; 0]. What is the resulting vector?
hard📝 Application Q8 of 15
Step-by-Step Solution
Solution:
Step 1: Calculate inverse of A
det(A) = (4*6) - (7*2) = 24 - 14 = 10
inv(A) = (1/10) * [6 -7; -2 4] = [0.6 -0.7; -0.2 0.4]Step 2: Multiply inv(A) by B
inv(A)*B = [0.6 -0.7; -0.2 0.4] * [1; 0] = [0.6*1 + (-0.7)*0; -0.2*1 + 0.4*0] = [0.6; -0.2]Final Answer:
[0.6; -0.2] -> Option AQuick Check:
Inverse times vector = [0.6; -0.2] [OK]
Quick Trick: Multiply inv(A) by vector to solve linear systems [OK]
Common Mistakes:
- Forgetting to multiply by inverse
- Incorrect determinant calculation
- Mixing up matrix multiplication order
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