JAMIA 2024 — Mathematics PYQ

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Question

JAMIA 2024 — Mathematics PYQ

JAMIA | Mathematics | 2024

A matrix $A = [a_{ij}]_{m \times n}$ is said to be symmetric if

Choose the correct answer:

Explanation

Mathematical Condition:

Ek matrix $A = [a_{ij}]_{m \times n}$ symmetric hone ke liye do shartein (conditions) zaroori hain:

Square Matrix: Matrix ka square matrix hona zaroori hai, yaani $m = n$ .
Elements ki Condition: Har element $a_{ij}$ apne corresponding element $a_{ji}$ ke barabar hona chahiye:

$a_{ij} = a_{ji}$

Example:

Maan lijiye ek $2 \times 2$ matrix $A$ hai:

A = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}

Yahan $a_{12} = 2$ aur $a_{21} = 2$ hai, isliye $a_{12} = a_{21}$ . Agar aap iska transpose lenge:

A^T = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}

Kyonki $A^T = A$ , isliye yeh ek Symmetric Matrix hai.

Final Answer:

Aapke sawal ka sahi jawab niche di gayi condition hai:

\mathbf{a_{ij} = a_{ji}}