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M is a matrix with real entries given by...

M is a matrix with real entries given by `M=[{:(4,k,0),(6,3,0),(2,t,k):}]`
Which of the following conditions guarantee the invertivility of M ?
1. `k ne 2`
2. `k ne 0`
3. `t ne 0`
4. `t ne 1`
Select the correct answer using the code given below :

A

1 and 2

B

2 and 3

C

1 and 4

D

3 and 4

Text Solution

Verified by Experts

The correct Answer is:
A
As given `M=[{:(4,k,0),(6,3,0),(2,t,k):}]`
M will be invertible, if
`[{:(4,k,0),(6,3,0),(2,t,k):}]ne 0`
`rArr k ne 0 or k (12-6k) ne 0`
`rArr k ne 0, k ne 2`
Thus, statement (1) and (2) are correct.
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