JAMIA 2023 — Mathematics PYQ

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Question

JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

If the rank of matrix $a 00 am p; 0 am p; b am p; 0 am p; 0 am p; 0 am p; c$ is $2$ , then

Choose the correct answer:

Explanation

1. Given Matrix:

A = \begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}

2. Property of Rank for a Diagonal Matrix:

Ek diagonal matrix ka rank uske non-zero diagonal elements ki sankhya (count) ke barabar hota hai.

3. Case 1: Agar Rank = 3 ho (Full Rank):

Iska matlab hai ki teeno elements ( $a, b, c$ ) non-zero hone chahiye.

\text{Condition: } a \neq 0, b \neq 0, c \neq 0 \implies abc \neq 0

4. Case 2: Agar Rank = 2 :

Iska matlab hai ki koi bhi do elements non-zero honge aur ek element zero hoga.

\text{Condition: } abc = 0