If A = axya and if xy = 1, then det (AAT) is equal to
a2 - 1
(a2 + 1)2
1 - a2
(a2 - 1)2
D.
Given, A = axya∴ AT = ayxa∴ AAT = axyaayxa = a2 + x2ay + axay + axy2 + a2∴ detAAT = a2 + x2ay + axay + axy2 + a2= a2x2 + y2 + x2y2 + a4 - ay + ax2= a2x2 + y2 + 1 + a4 - a2y2 + a2x2 + 2a2yx ∵ xy = 1 as given= a2x2 + y2 + 1 + a4 - a2x2 + y2 - 2a2yx= 1 - 2a21 + a4= a2 - 12
If A = xx - 12x1 and if det A = - 9, then the avlue of x are
32, - 3
- 23, 3
23, 3
- 32, 3
The value of the determinant sin236°cos236°cot135°sin253°cot135°cos253°cot135°cos225°cos265° is
- 2
- 1
0
1
If A = x1- x01- 1x07 and det(A) = 3012- 10067, then value of x is
- 3
3
2
- 8
The coefficient of x2 in the expansion of the determinnat x2x3 + 1x5 + 2x3 + 3x2 + xx3 + x4x + 4x3 + x423 is
- 10
- 6
Let A = 1- 1 - i32- 1 + i321. Then A100 is equal to
2100A
299A
298A
A
If f(x) = xx2x312x3x2026x, then f'(x) is equal to
x3 + 6x2
6x3
3x
6x2
If A = 4kk0kk00k and det(A) = 256, then k equals
4
5
6
8
If A = 1011, then An + nI is equal to
I
nA
I + nA
I - nA
If A = 1111, then A2017 is equal to
22015A
22016A
22014A
22017A