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JAMIA 2025 — Mathematics PYQ

JAMIA | Mathematics | 2025

The determinant of a diagonal matrix is :

Choose the correct answer:

Explanation

Mathematical Representation

Agar hamare paas ek $n \times n$ order ki diagonal matrix $A$ hai:

A = \begin{bmatrix} d_1 & 0 & \dots & 0 \\ 0 & d_2 & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & d_n \end{bmatrix}

Toh iska determinant $|A|$ niche diye gaye formula se nikala jata hai:

|A| = d_1 \times d_2 \times \dots \times d_n

Example

Agar matrix $A$ niche di gayi hai:

A = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \end{bmatrix}

Toh iska determinant hoga:

|A| = 5 \times 3 \times 2

|A| = 30

Short Answer: Product of its diagonal elements.