Given A = [1 2; 3 4] and b = [5; 11], what is the output of x = A\b?

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MATLAB - Linear Algebra

Given A = [1 2; 3 4] and b = [5; 11], what is the output of x = A\b?

A[3; 1]

B[2; 1]

C[1; 2]

D[0; 5]

Step-by-Step Solution

Solution:

Step 1: Write the system of equations
From A\b, solve:
1*x1 + 2*x2 = 5
3*x1 + 4*x2 = 11
Step 2: Solve the system manually
Multiply first equation by 3:
3*x1 + 6*x2 = 15
Subtract second equation:
(3*x1 + 6*x2) - (3*x1 + 4*x2) = 15 - 11
2*x2 = 4 => x2 = 2
Substitute x2=2 in first:
x1 + 2*2 = 5 => x1 = 1
Final Answer:
[1; 2] -> Option C
Quick Check:
Solution vector x = [1; 2] [OK]

Quick Trick: Solve equations stepwise or use A\b directly [OK]

Common Mistakes:

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