A consistent system has three linear equations in two unknowns. Which rank condition gives it a unique solution?
Correct answer: B. rank(A) = 2 and rank([A|B]) = 2
- A. rank(A) = 1 and rank([A|B]) = 1
- B. rank(A) = 2 and rank([A|B]) = 2
- C. rank(A) = 3 and rank([A|B]) = 2
- D. rank(A) = 2 and rank([A|B]) = 3
Explanation
A unique solution requires the rank of the coefficient matrix to equal the rank of the augmented matrix and to equal the number of unknowns. Here that number is two, so both ranks must be 2.
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