For a 3 x 3 matrix A = [a_ij], whose element a_ij is given by a_ij = √(i^2 + 3j) then what is element a_31? Option 1: √6 Option 2: √7 Option 3: 2√3 Option 4: 2√2

Answer: 2√3. Solution: Substitute i = 3, j = 1 in a_ij = √(i^2 + 3j): a_31 = √(9 + 3) = √12 = 2√3.

Applied Mathematics

Algebra

Easy

applied

For a 3 $\times$ 3 matrix A = [a $_{ij}$ ], whose element a $_{ij}$ is given by $a_{ij} = \sqrt{i^2 + 3j}$ then what is element a $_{31}$ ?

$\sqrt{6}$

$\sqrt{7}$

$2\sqrt{3}$

$2\sqrt{2}$

✅ Correct Option: 3

Substitute $i = 3, j = 1$ in $a_{ij} = \sqrt{i^2 + 3j}$ : $a_{31} = \sqrt{9 + 3} = \sqrt{12} = 2\sqrt{3}$ .

2023: 11 Aug Shift 1

If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$ , If $5Q - 3P + 2R = 0$ , then the matrix R is

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Evaluate $3^{15} \mod(7)$

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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:

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Solution for the inequality $|3x - 7| \leq 2$ is :

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The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

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The least positive integer X satisfying $28 \equiv x (\mod 6)$ is :

For a 3 ×\times× 3 matrix A = [aij_{ij}ij​], whose element aij_{ij}ij​ is given by aij=i2+3ja_{ij} = \sqrt{i^2 + 3j}aij​=i2+3j​ then what is element a31_{31}31​?

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CUET Mathematics Past Year Questions (Topic-Wise)

For a 3 $\times$ 3 matrix A = [a $_{ij}$ ], whose element a $_{ij}$ is given by $a_{ij} = \sqrt{i^2 + 3j}$ then what is element a $_{31}$ ?