TS EAMCET 2022 (Online) 18th July Evening Shift | Matrices and Determinants Question 92 | Mathematics

Let $x=\alpha, y=\beta, z=\gamma$ be the unique solution of the system of simultaneous linear equations $2 x+3 y-2 z+4=0,3 x-4 y+3 z+5=0$, $k x-2 y+z+3=0$. If $\alpha=-2$, then $k=$

$\left|\begin{array}{ll}1 & 2 \\ 3 & 5\end{array}\right|$

$\left|\begin{array}{ll}5 & 3 \\ 1 & 2\end{array}\right|$

$\left|\begin{array}{ll}3 & 5 \\ 1 & 2\end{array}\right|$

$\left|\begin{array}{ll}3 & 5 \\ 2 & 1\end{array}\right|$

TS EAMCET 2022 (Online) 18th July Evening Shift

MCQ (Single Correct Answer)

-0

If $\frac{x^2+7}{\left(x^2+1\right)(x-2)}=\frac{A}{x-2}+\frac{B x+C}{x^2+1}$, then the determinant of the matrix $\left[\begin{array}{ll}A & B \\ C & \frac{2}{5}\end{array}\right]$ is

-5

$94 / 25$

-2

TS EAMCET 2022 (Online) 18th July Morning Shift

MCQ (Single Correct Answer)

-0

3. Let $A=\left[\begin{array}{ccc}a & 3 & 5 \\ 5 & -1 & 3 \\ 2 & 3 & -4\end{array}\right]$ and $B=\left[\begin{array}{ccc}b & 1 & 4 \\ 4 & c & 1 \\ -3 & 1 & d\end{array}\right]$. If the trace of $A$ is -4 and $A B=\left[\begin{array}{ccc}-1 & 0 & 17 \\ -3 & 10 & 25 \\ 28 & -8 & 3\end{array}\right]$ then $a+b+c+d=$

-1

TS EAMCET 2022 (Online) 18th July Morning Shift

MCQ (Single Correct Answer)

-0

$\left|\begin{array}{ccc}1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3\end{array}\right|=$

$a^2 b^2(a-b)+b^2 c^2(b-c)+c^2 a^2(c-a)$

$a^2\left(b^3-c^3\right)+b^3\left(c^3-a^3\right)+c^2\left(a^3-b^3\right)$

$a^3\left(b^2-c^2\right)+b^3\left(c^2-a^2\right)+c^2\left(a^2-b^2\right)$

$a b\left(a^3-b^3\right)+b c\left(b^3-c^3\right)+c a\left(c^3-a^3\right)$

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