Let A be the matrix bmatrix 3 & -4 \\ 1 & -1 bmatrix. If A is expressed as the sum of P and Q, where P is a symmetric and Q is a skew symmetric matrix, then which of the following options define P and Q correctly? Option 1: P = bmatrix 3 & -3/2 \\ -3/2 & -1 bmatrix, Q = bmatrix 0 & -5/2 \\ 5/2 & 0 bmatrix Option 2: P = bmatrix 2 & -3/2 \\ -3/2 & -2 bmatrix, Q = bmatrix 1 & -5/2 \\ 5/2 & 1 bmatrix Option 3: P = bmatrix 3 & -5/2 \\ -3/2 & -1 bmatrix, Q = bmatrix 0 & -3/2 \\ 5/2 & 0 bmatrix Option 4: P = bmatrix 3 & -3/2 \\ -3/2 & -1 bmatrix, Q = bmatrix 2 & -5/2 \\ -5/2 & 1 bmatrix

The answer is 'P = bmatrix 3 & -3/2 \\ -3/2 & -1 bmatrix, Q = bmatrix 0 & -5/2 \\ 5/2 & 0 bmatrix'. View full solution:

CUET Mathematics - Let A be the matrix bmatrix 3 & -4 \\ 1 & -1 bmatrix. If A is expressed as the sum of P and Q, where P is a symmetric and Q is a skew symmetric matrix, then which of the following options define P and Q correctly? | PYQs + Solutions

CUET Mathematics 2026 19th May Shift 1

Algebra

Medium

core

$P = \begin{bmatrix} 3 & -\frac{3}{2} \\ -\frac{3}{2} & -1 \end{bmatrix}, Q = \begin{bmatrix} 0 & -\frac{5}{2} \\ \frac{5}{2} & 0 \end{bmatrix}$

$P = \begin{bmatrix} 2 & -\frac{3}{2} \\ -\frac{3}{2} & -2 \end{bmatrix}, Q = \begin{bmatrix} 1 & -\frac{5}{2} \\ \frac{5}{2} & 1 \end{bmatrix}$

$P = \begin{bmatrix} 3 & -\frac{5}{2} \\ -\frac{3}{2} & -1 \end{bmatrix}, Q = \begin{bmatrix} 0 & -\frac{3}{2} \\ \frac{5}{2} & 0 \end{bmatrix}$

$P = \begin{bmatrix} 3 & -\frac{3}{2} \\ -\frac{3}{2} & -1 \end{bmatrix}, Q = \begin{bmatrix} 2 & -\frac{5}{2} \\ -\frac{5}{2} & 1 \end{bmatrix}$

✅ Correct Option: 1

Related questions:

19 May Shift 1

If $A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -3 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 3 \\ 4 & -5 \\ 1 & 2 \end{bmatrix}$ , then which of the following statements are TRUE?

(A) AB is defined

(B) AB and BA both are defined and AB = I, where I is an identity matrix of order 2

(D) AB and BA both are defined and AB = BA

Choose the correct answer from the options given below:

15th May Shift 1

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$A = \begin{bmatrix}3 & 5\\ 5 & 2\end{bmatrix}$	I.	Scalar matrix
B.	$A = \begin{bmatrix}0 & -2\\ 2 & 0\end{bmatrix}$	II.	Upper triangular matrix
C.	$A = \begin{bmatrix}5 & 3\\ 0 & 4\end{bmatrix}$	III.	Symmetric matrix
D.	$A = \begin{bmatrix}3 & 0\\ 0 & 3\end{bmatrix}$	IV.	Skew symmetric matrix

Choose the correct answer from the options given below:

21 May Shift 2

Let A be a 3 × 7 matrix, then each column of A contains:

CUET Mathematics 2026 19th May Shift 1 PYQs

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