JEE MATHEMATICS MCQ: MATRICES

1 Easy

1 of 1

Application +4 | -1

Let

A=\left[\begin{array}{lll}a & b & c \\ p & q & r \\ x & y & z\end{array}\right]

and suppose that

\operatorname{det}(A)=2

, then

\operatorname{det}(B)

equals, where

B=\left[\begin{array}{ccc}4 x & 2 a & -p \\ 4 y & 2 b & -q \\ 4 z & 2 c & -r\end{array}\right]

View answer and explanation

Correct option: C

-16

Option C (-16) is correct because applying determinant properties such as row swapping and scalar multiplication leads to det(B) = -16.

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

a, b, c

a x+b y+c=0

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

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

ax + 2y - b = 0

\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|

\omega

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

A

2 \times 2

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

|A|