MATLAB - Linear Algebra
You have a non-square matrix
A = [1 2 3; 4 5 6] and vector b = [7; 8]. What does x = A\b compute in MATLAB?You have a non-square matrix A = [1 2 3; 4 5 6] and vector b = [7; 8]. What does x = A\b compute in MATLAB?
hard📝 Application Q15 of 15
Step-by-Step Solution
Solution:
Step 1: Recognize matrix shape and operation
A is 2x3 (more columns than rows), so system is underdetermined.Step 2: Understand MATLAB's backslash behavior for non-square A
MATLAB computes the least-squares solution x that minimizes ||Ax - b|| (minimum norm among solutions).Final Answer:
A least-squares solution minimizing ||Ax - b|| -> Option CQuick Check:
Backslash solves least-squares for non-square A [OK]
Quick Trick: Backslash gives least-squares solution if A not square [OK]
Common Mistakes:
- Expecting error for non-square A
- Thinking it calculates inverse always
- Assuming exact solution always exists
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