Applied Mathematics

Algebra

Medium

Matrix $A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is skew - symmetric, then the values of a, b c are :

a = -4 , b = 0 , c = -5

a = 4 , b = 0 , c = 5

a = -4 , b = 1 , c = -5

a = 4 , b = 1 , c = 5

✅ Correct Option: 1

For skew-symmetric matrix: $A^T = -A$ , meaning $a_{ij} = -a_{ji}$ and diagonal entries are 0.

Diagonal: $b = 0$ .

$a_{12} = -a_{21}$ : $a = -4$ .

$a_{13} = -a_{31}$ : $5 = -c \Rightarrow c = -5$ .

So $a = -4, b = 0, c = -5$ .

2023: 23 May Shift 3

The solution set of the inequation $\frac{7+5x}{4} \geq \frac{x}{3} - 10$ , $x \in \mathbb{R}$ is :

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	A matrix which is both symmetric and skew symmetric	I.	symmetric matrix
B.	All positive integral powers of a symmetric matrix	II.	unit matrix
C.	Positive odd integral powers of a skew-symmetric matrix	III.	null matrix
D.	A square matrix $A = [a_{ij}]_{n\times n}$ with $a_{ij} = \begin{cases}0, & \forall\, i \neq j \\ 1, & \forall\, i = j\end{cases}$	IV.	skew-symmetric matrix

Choose the correct answer from the options given below:

2023: 22 May Shift 3

A point $P(3a, -2b)$ lies in region $4x + 7y \leq (-3)$ which of the following options is true ?

2023: 11 Aug Shift 1

Let X & Y be 2 invertible square matrix, then which of the following is true

(A) $(AB)^{-1} = A^{-1} B^{-1}$

(B) $(AB)^{-1} = B^{-1} A^{-1}$

(D) $(AB)' = B' A'$

Choose the answer from the options given below

2022: 25 May Shift 1

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

2026: 14 May Shift 2

If A is a non-singular square matrix of order n, then which of the following are TRUE ?

A. $|adj A|=|A|^{n-1}$

B. $|adj A|=|A|^{n-2}$

C. $|adj (adj A)|=|A|^{(n-2)^2}$

D. $|adj (adj A)|=|A|^{(n-1)^2}$

Choose the correct answer from the options given below:

Matrix A=[0a54b−1c10]A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}A=​04c​ab1​5−10​​ is skew - symmetric, then the values of a, b c are :