isi-entrance 2017 Q11

isi-entrance · India · UGA Matrices Determinant and Rank Computation
A ``basic row operation'' on a matrix means adding a multiple of one row to another row. Consider the matrices $$A = \left(\begin{array}{rrr} x & 5 & x \\ 1 & 3 & -2 \\ -2 & -2 & 2 \end{array}\right) \quad \text{and} \quad B = \left(\begin{array}{rrr} 0 & 0 & 21 \\ 1 & -1 & -14 \\ 0 & \frac{4}{3} & 4 \end{array}\right)$$ It is given that $B$ can be obtained from $A$ by applying finitely many basic row operations. Then, the value of $x$ is:
(A) 3
(B) $-3$
(C) $-1$
(D) 2.
A ``basic row operation'' on a matrix means adding a multiple of one row to another row. Consider the matrices
$$A = \left(\begin{array}{rrr} x & 5 & x \\ 1 & 3 & -2 \\ -2 & -2 & 2 \end{array}\right) \quad \text{and} \quad B = \left(\begin{array}{rrr} 0 & 0 & 21 \\ 1 & -1 & -14 \\ 0 & \frac{4}{3} & 4 \end{array}\right)$$
It is given that $B$ can be obtained from $A$ by applying finitely many basic row operations. Then, the value of $x$ is:\\
(A) 3\\
(B) $-3$\\
(C) $-1$\\
(D) 2.