Let M denote the set of all real matrices of order $3 \times 3$ and let $...

Let A be a $3 \times 3$ matrix such that ${X^T}AX = O$ for all nonzero $3 \times 1$ matrices $...

If the system of equations
$2x - y + z = 4$
$5x + \lambda y + 3z = 12$
$...

If A,B, and $\left( {{\mathop{\rm adj}\nolimits} \left( {{{\rm{A}}^{ - 1}}} \right) + {\mathop{\rm adj}\nolimits} \left( {{{\rm{B}}^{ - 1}}} \right)} \right)$ are non-singular matrices of same...

If the system of equations
$(\lambda -1)\text{x}+(\lambda -4)\text{y}+\lambda \text{z}=5$
$\lambda \text{x}+(\lambda -1)\text{y}+(\lambda -4)\text{z}=7$
$(\lambda +1)\text{x}+(\lambda +2)\text{y}-(\lambda +2)\text{z}=9$
has infinitely many solutions, then $...