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JEE MATHEMATICS MCQ: MATRICES

1 Easy

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Analyzing +4 | -1

Let

a, b, c

be such that

b(a+c) \neq 0

. If

\left| {\begin{array}{cccccccccccccccccccc} a&{a + 1}&{a - 1} \\ { - b}&{b + 1}&{b - 1} \\ c&{c - 1}&{c + 1} \end{array}} \right| + \left| {\begin{array}{cccccccccccccccccccc} {a + 1}&{b + 1}&{c - 1} \\ {a - 1}&{b - 1}&{c + 1} \\ {{{( - 1)}^{n + 2}}a}&{{{( - 1)}^{n + 1}}b}&{{{( - 1)}^n}c} \end{array}} \right| = 0,

then the value of

n

is

View answer and explanation

Correct option: D

any odd integer

Option D (any odd integer) is correct because the equation simplifies to

2\left| {\begin{array}{cccccccccccccccccccc} a&{a + 1}&{a - 1} \\ { - b}&{b + 1}&{b - 1} \\ c&{c - 1}&{c + 1} \end{array}} \right| = 0

when n is odd.

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

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

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|

\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

2 \times 2

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

|A|