JEE MATHEMATICS MCQ: MATRICES

1 Easy

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Analyzing +4 | -1

Let

P=\left[\begin{array}{ccc}3 & -1 & -2 \\ 2 & 0 & a \\ 3 & -5 & 0\end{array}\right]

where

a \in R

, suppose

Q=\left[q_{i j}\right]_{3 \times 3}

Matrix such that

P Q=\mathrm{KI}_3

for some non-zero

K \in R

.If

q_{23}=\frac{-k}{8}

and

|Q|=\frac{k^2}{2}

, then

a^2+k^2

View answer and explanation

Correct option: B

Prime number

Option B (Prime number) is correct because after solving the equations derived from the given conditions, we find a = -1 and k = 4, so a² + k² = 17, which is a prime number.

More Questions from MATRICES

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\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

and

a, b, c

are real numbers then the line

a x+b y+c=0

passes through the fixed point is The number of solutions of the system of equations

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

is If the equations

2x + 3y + 1 = 0,3x + y - 2 = 0

and

ax + 2y - b = 0

are consistent, then The value of the determinant

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

, is If

\omega

is the cube root of unity, then

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

is equal to For any matrix

A

of order

2 \times 2

, if

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

, then

|A|

is equal to