Class 12Mathematics3 and 4 .Determinants and MatricesExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
EasyThe area of a triangle with vertices $A(k, 1)$,$B(2, 4)$,and $C(1, 1)$ is $6$ sq. units. Find the value of $k$.
- A$5$ and $3$
- B$-5$ and $3$
- C$3$ and $-1$
- D$5$ and $-3$
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If $A = \begin{bmatrix} x & 1 & 2 \\ 2 & 4 & x \\ -3 & 3 & 2 \end{bmatrix}$ is a singular matrix and the distinct values of $x$ are $x_1$ and $x_2$,then $x_1 + x_2 + x_1 x_2 = $.
If $A, B, C$ are the angles of a triangle,then the system of equations $-x + y \cos C + z \cos B = 0$,$x \cos C - y + z \cos A = 0$,$x \cos B + y \cos A - z = 0$ have
The value of $x,$ if $\left| \begin{matrix} -x & 1 & 0 \\ 1 & -x & 1 \\ 0 & 1 & -x \end{matrix} \right| = 0$ is equal to
Easy
View SolutionThe number of real values of $t$ such that the system of homogeneous equations
$\begin{aligned}
t x+(t+1) y+(t-1) z &=0 \\
(t+1) x+t y+(t+2) z &=0 \\
(t-1) x+(t+2) y+t z &=0
\end{aligned}$
has non-trivial solutions is
$\begin{aligned}
t x+(t+1) y+(t-1) z &=0 \\
(t+1) x+t y+(t+2) z &=0 \\
(t-1) x+(t+2) y+t z &=0
\end{aligned}$
has non-trivial solutions is
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