Given A = [4 2; 2 1] and b = [10; 5], you want to solve Ax = b but also check if the solution is unique. Which MATLAB approach helps you confirm uniqueness?
hard📝 Application Q9 of 15
MATLAB - Linear Algebra
Given A = [4 2; 2 1] and b = [10; 5], you want to solve Ax = b but also check if the solution is unique. Which MATLAB approach helps you confirm uniqueness?
AUse <code>x = pinv(A)*b;</code> to get unique solution
BSolve <code>x = A\b;</code> and ignore uniqueness
CUse <code>x = inv(A)*b;</code> without checking
DCheck if <code>det(A) != 0</code> before using <code>x = A\b;</code>
Step-by-Step Solution
Solution:
Step 1: Understand uniqueness condition
A unique solution exists if det(A) != 0, meaning A is invertible.
Step 2: Check determinant before solving
Calculate det(A). If nonzero, solve with x = A\b; confidently.
Final Answer:
Check if det(A) != 0 before using x = A\b; -> Option D
Quick Check:
Uniqueness check = det(A) != 0 [OK]
Quick Trick:Check det(A) before solving to confirm uniqueness [OK]
Common Mistakes:
Assuming pinv always gives unique solution
Ignoring determinant check
Using inv(A) without verifying invertibility
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