NDA Mathematics 4 September 2022 | Matrices Question 58 | Mathematics

Let A = $\left(\begin{array}{ccc}0 & \sin^2 \theta & \cos^2 \theta \\ \cos^2 \theta & 0 & \sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta & 0\end{array}\right)$ and A = P + Q where P is symmetric matrix and Q is skew-symmetric matrix.

What is Q equal to ?

$\left(\begin{array}{ccc}0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0\end{array}\right)$

$\left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right)$

cos 2θ$\left(\begin{array}{ccc}0 & −1 & 1 \\ 1 & 0 & −1 \\ −1 & 1 & 0\end{array}\right)$

cos 2θ$\left(\begin{array}{ccc}0 & −1/2 & 1/2 \\ 1/2 & 0 & −1/2 \\ −1/2 & 1/2 & 0\end{array}\right)$

NDA Mathematics 10 April 2022

MCQ (Single Correct Answer)

+2.5

-0.83

Consider the following in respect of the matrices:

A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \\ -m\end{bmatrix} $

1. CA = CB

2. AC = BC

3. C(A + B) = CA + CB

Which of the above statements is/are correct?

1 only

2 only

2 and 3

1 and 2

NDA Mathematics 10 April 2022

MCQ (Single Correct Answer)

+2.5

-0.83

If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix},$ then what is A(adj A) equal to?

(where) I is the identity matrix.

Null matrix

-I

NDA Mathematics 10 April 2022

MCQ (Single Correct Answer)

+2.5

-0.83

Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct?

1. AB = BA

2. AB is a scalar matrix

3. AB can be a null matrix

Select the correct answer using the code given below:

1 only

1 and 2 only

2 only

1, 2 and 3

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