Under which of the following condition(s), will the matrix `A=[{:(0,0,q),(2,5,1),(8,p,p):}]` be singular ?
1. q = 0 2. p = 0 3. p = 20
Select the correct answer using the code given below :

Options

A. 1 and 2
B. 3 only
C. 1 and 3
D. 1 or 3

Answer

D

Explanation

`A=[{:(0,0,q),(2,5,1),(8,p,p):}]`
Matrix A will be singular, when |A|=0, |A| will be zero when either one row or one column is zero.
(1) For q = 0
`A=[{:(0,0,0),(2,5,1),(8,p,p):}]`
`rArr |A|=0`
`therefore` A is singular.
(2) For p = 0
`A=[{:(0,0,q),(2,5,5),(8,0,0):}]`
`rArr |A|=q|{:(2,5),(8,0):}|=-40q`
`therefore` A is not singular.
(3) For p = 20
`|A|=q|{:(2,5),(8,20):}|=40 - 40 = 0`
`therefore` A is singular.
Thus codes (1) or (3) are correct.