BITSAT 2024 Shift 1 Paper

Given the matrix A=[

3	−2	4
1	2	−1
0	1	1

] and A−1=‌

1

k

‌adj(A), we want to determine the value of k.
We know from the properties of matrices that:
A−1=‌

adj(A)

|A|

By comparing this equation with the given relationship A−1=‌

1

k

‌adj(A), we can identify that:
k=|A|
Therefore, we need to calculate the determinant |A| of the matrix A :
|A|=|

3	−2	4
1	2	−1
0	1	1

|
To find |A|, expand across the first row:
|A|=3|

2	−1
1	1

|−(−2)|

1	−1
0	1

|+4|

1	2
0	1

|
Calculate each of the 2×2 determinants:
‌|

2	−1
1	1

|=(2×1)−(−1×1)=2+1=3
‌|

1	−1
0	1

|=(1×1)−(0×−1)=1
‌|

1	2
0	1

|=(1×1)−(0×2)=1
Substitute these values back into the determinant calculation:

|A|=3×3+2×1+4×1=9+2+4=15
Thus, the value of k is |A|=15.