List of top Mathematics Questions on Matrix asked in AP EAMCET

Let $ A $ be a $ 4 \times 4 $ matrix and $ P $ be its adjoint matrix. If $ |P| = \left| \frac{A}{2} \right| $, then $ |A^{-1}| = ? $

If the matrix is:
$\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?$

If $ \alpha, \beta, \gamma $ are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then $ \alpha \beta + \beta \gamma + \gamma \alpha $ is:

If $ A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} $ is a singular matrix, then the quadratic equation having the roots $ k $ and $ \frac{1}{k} $ is:

If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ (AA^T) $ and $ (A - A^T) $ is:

While solving a system of linear equations $ AX = B $ using Cramer’s rule, if \includegraphics[]{6.png}

If $ A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix} $ and $ \alpha^2 + \beta A = 21 $ for some $ \alpha, \beta \in \mathbb{R} $, then find $ \alpha + \beta $:

If $ A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] $, then $\text{det} (A - A^T) = $:

If the system of equations: $$ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 $$ has only the trivial solution, then the rank of the matrix: \[\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right] \] is

Evaluate the following determinant: $ \begin{vmatrix} 1 & 1 & 1 \\ a^2 & {b^2} & {c^2} \\ {a^3} & {b^3} & {c^3} \\ \end{vmatrix} $

Assertion (A): If $ B $ is a $ 3 \times 3 $ matrix and $ |B| = 6 $, then $ | {Adj}(B) | = 36 $.
Reason (R): If $ B $ is a square matrix of order $ n $, then $ |{Adj}(B)| = |B|^n $.

The system of equations $ x + 2y + 3z = 6 $, $ x + 3y + 5z = 9 $, $ 2x + 5y + az = 12 $ has no solution when $ a = $: