IIT-JEE 2010 · Paper 1 · Mathematics Q33

← IIT-JEE 2010 · Paper 1

MathematicsSingle correct+3 / -1Question 33 of 84

The number of $3\times3$ matrices A whose entries are either 0 or 1 and for which the system $A\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$ has exactly two distinct solutions, is

2^9-1

168

Answer and worked solution

Official answer: A

Linear systems have no solution, exactly one, or infinitely many. If $X_1\ne X_2$ both solve $AX=B$ , then $A(X_1-X_2)=0$ and every $X_1+t(X_1-X_2)$ is also a solution. So no matrix gives exactly two solutions.

(A) 0

Topics:Systems of linear equations

← Previous question Next question →

IIT-JEE 2010 · Paper 1, Mathematics question 33