Which one of the following options is incorrect?

For a square matrix A in the matrix equation AX = B.

Question

Question

This question was previously asked in

CUET UG Official Maths Paper (Held on_23 May 23)

Answer 1

Explanation:

Matrix equation is Ax = B where A is square matrix and B is column matrix.

Then if |A| ≠ 0, then there exists a unique solution.

If |A| = 0 and (adj A)B ≠ 0 then there is no solution i.e., inconsistent.

If |A| = 0 and (adj A)B = 0 then system has infinitely many solutions i.e., consistent.

Hence the incorrect statement is "If |A| ≠ 0 and (adj A)B ≠ 0 then there is no solution."

Option (3) is true.

Download Solution PDF