CUET Preparation Today
Which one of the following options is incorrect? For a square matrix A in the matrix equation AX = B. |
If $|A| \neq 0$, then there exists a unique solution If $|A|=0$ and $(adj A) B \neq 0$ then there is no solution If $|A| \neq 0$ and $(adj A) B \neq 0$ then there is no solution If $|A|=0$ and $(adj A) B=0$ then system has infinitely many solutions |
If $|A| \neq 0$ and $(adj A) B \neq 0$ then there is no solution |
for AX = B 1 → |A| $\neq 0 \Rightarrow$ unique soln → correct 2 →|A| = 0 (Adj } A) B \neq 0 \Rightarrow$ no solution → correct 3 → |A| $neq 0$ (Adj A) B $\neq 0 \Rightarrow$ no solution → incorrect 4 → |A| = 0 $\Rightarrow$ (adj A)B = 0 $\Rightarrow$ infinite soln → correct |
