MCQ
Which of the following is correct?
- ADeterminant is a square matrix
- BDeterminant is a number associated to a matrix
- ✓Determinant is a number associated to a square matrix
- DNone of these
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$x+2 y+3 z=\alpha$
$4 x+5 y+6 z=\beta$
$7 x+8 y+9 z=\gamma-$
is consistent. Let $| M |$ represent the determinant of the matrix
$M=\left[\begin{array}{ccc}\alpha & 2 & \gamma \\ \beta & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$
Let $P$ be the plane containing all those $(\alpha, \beta, \gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0,1,0)$ from the plane $P$.
($1$) The value of $| M |$ is
($2$) The value of $D$ is