If A =  and A adj A = AA^T, then 5a +b is equal to

• -1

• 5

• 4

• 4

The system of linear equations x+λy−z=0; λx−y−z=0; x+y−λz=0 has a non-trivial solution for

• infinitely many values of λ.

• exactly one value of λ.

• exactly two values of λ.

• exactly two values of λ.

A =  is a matrix satisfying the equation AA^T = 9I, Where I is 3 x 3 identity matrix, then the ordered pair (a,b) is equal to

• (2,-1)

• (-2,1)

• (2,1)

• (2,1)

The set of all values of λ for which the system of linear equations 

2x₁-2x₂+x₃ = λx₁
2x₁- 3x₂ + 2x₃ = λx₂
-x₁ + 2x₂ = λx₃
a non- trivial solution.

• is an empty set

• is a singleton set

• contains two elements

• contains two elements

5.

If α, β ≠ 0 and f(n) = αⁿ+ βⁿ and 


= K(1-α)²(1-β)²(α- β)², then K is equal to 

• αβ 

• 1/αβ 

• 1

• 1

If A is a 3x3 non- singular matrix such that AA^T = A^TA, then BB^T is equal to

• l +B
• l

• B^-1

• B^-1

Let P and Q be 3 × 3 matrices with P ≠ Q. If P³= Q³ and P²Q = Q²P, then determinant of(P²+ Q²) is equal to

• -2

• 1

• 0

• 0

The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is:

• 3

• 2

• 1

• 1

Consider the system of linear equation
x¹ + 2x² + x³ = 3
2x¹ + 3x² + x³ = 3
3x¹ + 5x² + 2x³ = 1
The system has

• infinite number of solutions

• exactly 3 solutions

• a unique solution

• a unique solution

Let A be a 2 × 2 matrix with non-zero entries and let A2 = I, where I is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.
Statement-1: Tr(A) = 0.
Statement-2: |A| = 1.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.