In a square matrix the minor M_ij and the co-factor A_ij of and element a_ij are related by _____

If A is a non-singular matrix then IA^-1| = ______

If A = [2 0 1] then the rank of AA^T is ______

Cramer's rule is applicable only when ______

In the non - homogeneous system of equations with 3 unknowns if \(\rho\) (A) = \(\rho\) ([AIB]) = 2, then the system has _______

Every homogeneous system ______

Which of the following is not an elementary transformation?

If \(\rho\) (A) = \(\rho\) ([A/B]) = number of unknowns, then the system is _________--

The system of equations x + 2y + 3z = 1, x - y + 4z = 0, 2x + y + 7z = 1 has ___________

If A is a matrix of order m \(\times\) n, then \(\rho\) (A) is _________

If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2 is inconsistent then k is ___________

If A is a square matrix that IAI = 2, than for any positive integer n, |Aⁿ| = _______

If A^T is the transpose of a square matrix A, then ___________

Let A be a 3 \(\times\) 3 matrix and B its adjoint matrix If |B| = 64, then |A| = ___________

The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if _________

The augmented matrix of a system of linear equations is \(\left[\begin{array}{cccc} 1 & 2 & 7 & 3 \\ 0 & 1 & 4 & 6 \\ 0 & 0 & \lambda-7 & \mu+5 \end{array}\right]\). The system has infinitely many solutions if

If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

If \(\rho\) (A) = \(\rho\)([A| B]), then the system AX = B of linear equations is

If x^a y^b = e^m, x^c y^d = eⁿ, Δ₁ = \(\left| \begin{matrix} m & b \\ n & d \end{matrix} \right| \), Δ₂ = \(\left| \begin{matrix} a & m \\ c & n \end{matrix} \right| \), Δ₃ = \(\left| \begin{matrix} a & b \\ c & d \end{matrix} \right| \), then the values of x and y are respectively,

If A^TA⁻¹ is symmetric, then A² =

If A, B and C are invertible matrices of some order, then which one of the following is not true?

If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

If A is a 3 \(\times\) 3 non-singular matrix such that AA^T = A^TA and B = A^-1A^T, then BB^T =