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 ______

In the system of liner equations with 3 unknowns If \(\rho\) (A) = \(\rho\) ([A|B]) =1, the system has ________

In the system of equations with 3 unknowns, if Δ = 0, and one of Δ_x, Δ_y of Δ_z is non zero then the system is ______

In a homogeneous system if \(\rho\) (A) =\(\rho\) ([A|0]) < the number of unknouns then the system has ________

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 _______

If \(\rho\) (A) ≠ \(\rho\) ([AIB]), then the system is _____________

Every homogeneous system ______

If \(\rho\) (A) = r then which of the following is correct?

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 A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) 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 of order n, then |adj A| = ______________

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if __________

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

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

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| = ___________

If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then _____________

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 _________