Matrices and De...

Let a =  , then Det. A is

If A ’is the transpose of a square matrix A , then

The roots of the equation det.   are

If A is a symmetric matrix, then A^t  =

 is equal to  

If A is a non singular matrix of order 3 , then  |adj(A³ )| =

Let A =   B = [ B ₁, B ₂, B ₃], where B ₁, B ₂, B ₃are column matrices, and  
If α= |B| and βis the sum of all the diagonal elements of B, then α³+ β³is equal to

The values of α , for which   lie in the interval

Let for any three distinct consecutive terms a, b, c of an A.P, the lines ax + by + c = 0 be concurrent at the point P and Q(α, β) be a point such that the system of equations
x + y + z = 6,
2x + 5y + αz = βand
x + 2y + 3z = 4,
has infinitely many solutions. Then (PQ)²is equal to ____.

If f(x) =  then (1/5) f '(0) is equal to

Consider the system of linear equations
x + y + z = 4 μ,
x + 2y + 2 λz = 10 μ,
x + 3y + 4 λ²z = μ²+ 15
where λ, μ∈R.
Which one of the following statements is NOT correct?

If  I₃ is the identity matrix of order 3 , then  1₃⁻¹  is

Consider the system of linear equations
x + y + z = 5,
x + 2y + λ²z = 9,
x + 3y + λz = μ, where λ, μ∈R.
Then, which of the following statement is NOT correct?

If the system of linear equations
x - 2y + z = -4
2x + αy + 3z = 5
3x - y + βz = 3
has infinitely many solutions, then 12 α+ 13 βis equal to

A square matrix A is invertible iff det A is equal to

If f(x) =  for all x ∈R, then 2f(0) + f '(0) is equal to

If the system of equations
2x + 3y - z = 5
x + αy + 3z = -4
3x - y + βz = 7
has infinitely many solutions, then 13 αβis equal to

If the entries in a 3 x 3 determinant are either 0 or 1 , then the greatest value of this determinant is :

The system of equations given is:x + 2y + 3z = 34x + 3y - 4z = 48x + 4y - λz = 9 + μThe question asks for the ordered pair (λ, μ) when the system has infinitely many solutions.

Let S ₁and S ₂be respectively the sets of all a ∈ℝ- {0} for which the system of linear equations
ax + 2ay - 3az = 1
(2a + 1)x + (2a + 3)y + (a + 1)z = 2
(3a + 5)x + (a + 5)y + (a + 2)z = 3
has unique solution and infinitely many solutions. Then

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

The given system of equations is:
ax + 2y + z = 1
2ax + 3y + z = 1
3x + ay + 2z = β
For some α, β∈ℝ. The question asks which of the following is NOT correct.