Question

The system AX = B of n equations in n unknowns has infinitely many solutions if

• A. det A ≠ 0
• B. det A = 0, (adjA)B ≠ O
• C. det A = 0, (adjA)B = O
• D. det A ≠ 0, (adjA)B = O

Answer 1

Answer: (C)

det A = 0, (adjA)B = O

Answer 2

X = A^–1B

X = $\frac{(adjA).B}{|A|}$

Clearly if the system has infinite solutions |A| = 0 and

(adj A)B = O