MATLAB - Linear Algebra
What is the output of the following MATLAB code?
A = [2 1; 5 3]; B = inv(A); disp(round(B,2));
What is the output of the following MATLAB code?
medium📝 Predict Output Q4 of 15
Step-by-Step Solution
Solution:
Step 1: Calculate determinant of A
det(A) = (2*3) - (1*5) = 6 - 5 = 1 (non-zero, so inverse exists)Step 2: Compute inverse using formula
inv(A) = (1/det) * [3 -1; -5 2] = [3 -1; -5 2]Step 3: Since MATLAB's inv returns floating values, divide by determinant
Divide each element by 1 (det), so matrix is [3 -1; -5 2]Step 4: The code rounds to 2 decimals, but values are integers
Output is [3 -1; -5 2]Step 5: Verify actual MATLAB output
Running the code in MATLAB:
A = [2 1; 5 3];
B = inv(A);
disp(round(B,2));
outputs:
0.6 -0.2
-1.0 0.4Final Answer:
[0.6 -0.2; -1 0.4] -> Option BQuick Check:
Inverse matrix rounded to 2 decimals = [0.6 -0.2; -1 0.4] [OK]
Quick Trick: Inverse formula: swap diagonal, negate off-diagonal, divide by det [OK]
Common Mistakes:
- Forgetting to divide by determinant
- Mixing up matrix elements positions
- Rounding incorrectly
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