If $D_1$ and $D_2$ are two $3 \times 3$ diagonal matrices, then
$D_1D_2$ is a diagonal matrix
$D_1D_2 = D_2D_1$
$D_1^2 + D_2^2$ is a diagonal matrix
All of the bove
If $2x + 3y - 5z = 7, \,x + y + z = 6$, $3x - 4y + 2z = 1,$ then $x =$
The value of $a$ for which the system of equations
$a^3x + ( a + 1)^3y + (a + 2)^3z = 0$ ; $ax + (a + 1) y + ( a + 2) z = 0$ ; $x + y + z = 0$, has a non zero solution is
The value of $\lambda $ for which the system of equations $2x - y - z = 12,$ $x - 2y + z = - 4,$ $x + y + \lambda z = 4$ has no solution is
If $x = cy + bz,\,\,y = az + cx,\,\,z = bx + ay$ (where $x, y, z $ are not all zero) have a solution other than $x = 0$, $y = 0$, $z = 0$ then $a, b$ and $ c $ are connected by the relation
Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(-2,0),(0,4),(0, \mathrm{k})$