MATLAB - Linear Algebra
Given
A = [2 1; 3 4] and b = [5; 10], what is the result of x = A\b?Given A = [2 1; 3 4] and b = [5; 10], what is the result of x = A\b?
medium📝 Predict Output Q13 of 15
Step-by-Step Solution
Solution:
Step 1: Write the system of equations
2x1 + x2 = 5
3x1 + 4x2 = 10.Step 2: Solve using elimination
Multiply first equation by 4: 8x1 + 4x2 = 20.
Subtract second: 5x1 = 10 -> x1 = 2.
Substitute: x2 = 5 - 2*2 = 1.Step 3: Verify solution
A*[2; 1] = [2*2 + 1*1; 3*2 + 4*1] = [5; 10] = b.Final Answer:
[2; 1] -> Option DQuick Check:
A\b = [2; 1] [OK]
Quick Trick: Use A\b to get exact solution vector [OK]
Common Mistakes:
- Miscalculating substitution (e.g., picking [1; 2])
- Confusing with matrix multiplication A*b
- Selecting x = b
Master "Linear Algebra" in MATLAB
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore MATLAB Quizzes