The system AX = B of n equations in n un

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

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

Options:

det A ≠ 0

det A = 0, (adj A)B ≠ O

det A = 0, (adj A)B = O

det A ≠ 0, (adj A)B = O

Correct Answer:

det A = 0, (adj A)B = O

Explanation:

X = A^–1B

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

Clearly if the system has infinite solutions

|A| = 0 and (adj A)B = O

Hence (3) is the correct answer.