JEE MATHEMATICS MCQ: MATRICES

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Analyzing +4 | -1

Let

A=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right], X=\left[\begin{array}{l}x_1 \\ x_2\end{array}\right], Y=\left[\begin{array}{l}y_1 \\ y_2\end{array}\right]\left(X^1, Y^1\right.

denote the transpose of

X

and

\left.Y\right)

Assertion:- If A is symmetric then

X^1 A Y=Y^1 A X

for each pair of

X

and

Y

Reason:-

X^1 A Y=Y^1 A X

for each pair of

X

and

\mathrm{Y}

then A is symmetric

View answer and explanation

Correct option: B

Both Assertion and Reason are true but Reason is not the correct explanation of Assertion

Option B (Both Assertion and Reason are true but Reason is not the correct explanation of Assertion) is correct. The assertion is true because if A is symmetric,

X^TAY = Y^TAX

. The reason is also true, but it's not the correct explanation.

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