JEE MATHEMATICS MCQ: MATRICES

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Analyzing +4 | -1

\Delta_{\mathrm{r}}=\left|\begin{array}{ccc}\mathrm{r} & 2 \mathrm{r}-1 & 3 \mathrm{r}-2 \\ \frac{\mathrm{n}}{2} & \mathrm{n}-1 & \mathrm{a} \\ \frac{1}{2} \mathrm{n}(\mathrm{n}-1) & (\mathrm{n}-1)^2 & \frac{1}{2}(\mathrm{n}-1)(3 \mathrm{n}-4)\end{array}\right|

then the value of

\sum_{\mathrm{r}=1}^{\mathrm{n}-1} \Delta_{\mathrm{r}}

View answer and explanation

Correct option: D

is independent of both a and n

Option D (is independent of both a and n) is correct because the summation of the determinants results in a determinant with two identical rows, making its value zero, thus independent of a and n.

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