List of top Mathematics Questions on Matrices and Determinants asked in TS EAMCET

If $A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2 \end{pmatrix}$, then $\sqrt{|\text{Adj}(AB)|} =$

The number of real values of 'a', for which the system of equations $2x+3y+az = 0$, $x+ay-2z=0$ and $3x+y+3z = 0$ has nontrivial solutions is

A is a $3 \times 3$ matrix satisfying $A^3 - 5A^2 + 7A + I = 0$. If $A^5 - 6A^4 + 12A^3 - 6A^2 + 2A + 2I = lA + mI$, then $l + m =$

If $A = \begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1 \end{pmatrix}$, $A^{-1} = \frac{1}{2} \begin{pmatrix} 1 & -1 & 1 \\ -8 & 6 & 2y \\ 5 & -3 & 1 \end{pmatrix}$ then the point $(x,y)$ lies on the curve

Consider a homogeneous system of three linear equations in three unknowns represented by $AX=O$. If $X = \begin{pmatrix}l \\ m \\ 0 \end{pmatrix}, l \neq 0, m \neq 0, l, m \in \mathbb{R}$ represents an infinite number of solutions of this system, then rank of A is

If the system of simultaneous linear equations $x - 2y + z = 0$, $2x + 3y + z = 6$ and $x + 2y + pz = q$ has infinitely many solutions, then

If the system of linear equations $(\sin\theta)x - y + z = 0$, $x - (\cos\theta)y + z = 0$, $x + y + (\sin\theta)z = 0$ has a non-trivial solution, then the least positive value of $\theta$ is

If $A = \begin{pmatrix} 1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3 \end{pmatrix}$, then $|(\text{Adj A})^{-1}| =$

If \( \left| \begin{matrix} 1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3 \end{matrix} \right| = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D+A = \)

If \( A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\0 & 1 & 2 \end{bmatrix} \), then \( \text{tr}(A) - \text{tr}(B) = \)

A, C are \( 3 \times 3 \) matrices. B, D are \( 3 \times 1 \) matrices. If \( AX=B \) has a unique solution and \( CX=D \) has an infinite number of solutions, then

A and B are two non-square matrices. If \( P = A + B \), \( Q = A^TB \), \( R = AB^T \), then the matrices whose order is equal to the order of A are

The sum of all the roots of the equation $\begin{vmatrix} x & -3 & 2 \\ -1 & -2 & x-1 \\ 1 & x-2 & 3 \end{vmatrix} = 0$ is

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then Adj(Adj(Adj A)) =

The system of linear equations $(\sin\theta)x+y-2z=0$, $2x-y+(\cos\theta)z = 0$ and $-3x+(\sec\theta)y+3z=0$, where $\theta \neq (2n+1)\frac{\pi}{2}$, has non-trivial solution for

If the system of simultaneous linear equations $x+\lambda y-2z=1$, $x-y+\lambda z=2$ and $x-2y+3z=3$ is inconsistent for $\lambda = \lambda_1$ and $\lambda_2$, then $\lambda_1 + \lambda_2 =$