Q. Let $A = \ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 0 & 5 \\ 0 & 2 & 1 \end{bmatrix}$ and$B = \ \begin{bmatrix} 0 \\ - 3 \\ 1 \end{bmatrix}$. Which of the following is true?
A) $AX = B$ has a unique solution
B) $AX = B$ has exactly three solutions
C) $AX = B$ has infinity many solutions
D) $AX = B$ is inconsistent
Explanation
(a)
$|A| = 1(0 - 10) - 2(2 - 6) + 3(4 - 0)$
$= - 10 + 8 + 12 = 10$
$\Rightarrow |A| \neq 0$
$\Rightarrow$Unique solution
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.