UPSC NDA Math Model Paper 6

Given, matrix is [

α	14	−1
2	3	1
6	2	3

]
If the determinant of the matrix is zero, then it will not have an inverse
Put α=1, then |A|=|

1	14	−1
2	3	1
6	2	3

| =21
Put α=−1, then |A|=|

−1	14	−1
2	3	1
6	2	3

| =7
Put α=0, then |A|=|

0	14	−1
2	3	1
6	2	3

| =14
Put α=−2, then |A|=|

−2	14	−1
2	3	1
6	2	3

| =0
Here, the the determinant of the matrix is zero for α=−2
Hence, if the inverse of the matrix [

α	14	−1
2	3	1
6	2	3

] does not exist then the value of α is 2