List of top Mathematics Questions on Matrices asked in AP EAPCET

If \[ A= \begin{bmatrix} c & -a & b\\ a & b & -c\\ -b & c & a \end{bmatrix}, \qquad B= \begin{bmatrix} 1 & 0 & 2\\ 0 & 1 & 2\\ 1 & 2 & 0 \end{bmatrix} \] and \[ AB= \begin{bmatrix} 4 & 4 & -2\\ 1 & 1 & 10\\ -1 & 5 & -4 \end{bmatrix}, \] then \(a^2+b^2+c^2=\)
If \[ A= \begin{bmatrix} 2 & -3 & 1\\ -3 & 1 & -2\\ 1 & -2 & 3 \end{bmatrix}, \] then \(\operatorname{Adj}(A)=\)
Let \(A\) be a \(3\times3\) matrix such that \[ AA^{T}=I_3. \] Then \(A\) is:
Let \[ A = \begin{bmatrix} 0 & k & k \\ k & -4 & -6 \\ k & -3 & -5 \end{bmatrix} \text{be a singular matrix for} \]
A value of \( \theta \) lying between \( 0 \) and \( \dfrac{\pi}{2} \) and satisfying \[ \begin{vmatrix} 1 + \sin^2 \theta & \cos^2 \theta & 4\sin 4\theta \\ \sin^2 \theta & 1 + \cos^2 \theta & 4\sin 4\theta \\ \sin^2 \theta & \cos^2 \theta & 1 + 4\sin 4\theta \end{vmatrix} = 0 \] is:
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
If $a$ is the determinant of the adjoint of the matrix $\begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3 \end{bmatrix}$ and $b$ is the determinant of the inverse of the matrix $\begin{bmatrix} 2 & 1 & 3 \\ 1 & -4 & -1 \\ 2 & 1 & 4 \end{bmatrix}$, then $\frac{b+1}{18b} = $
If \( t_n = \dfrac{1}{n(n+2)} \), \( n \in \mathbb{N} \), then which one of the following is true?
Assertion (A): \[ t_1 + t_2 + \cdots + t_{2003} = \dfrac{2003}{3005} \]
Reason (R): \[ t_n = \dfrac{1}{n(n+2)} = \dfrac{1}{2} \left( \dfrac{1}{n} - \dfrac{1}{n+2} \right) \]
If $2.5 + 5.9 + 8.13 + 11.17 + \ldots$ to $n$ terms = $an^3 + bn^2 + cn + d$, then find $a - b - c - d$
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
If the values \( x = \alpha, y = \beta, z = \gamma \) satisfy all the 3 equations \(x+2y+3z=4\), \(3x+y+z=3\) and \(x+3y+3z=2\), then \(3\alpha + \gamma = \)
If the values \( x = \alpha, y = \beta, z = \gamma \) satisfy all the 3 equations \(x+2y+3z=4\), \(3x+y+z=3\) and \(x+3y+3z=2\), then \(3\alpha + \gamma = \)
If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true? \[ \begin{cases}
If \[ A = \begin{bmatrix} 1 & 2 & -2 \\ 2 & -1 & 2\\ -1 & 1 & -2 \end{bmatrix}, \] then find $A + 2A^{-1}$.
The remainder obtained when \( (2m + 1)^{2n} \), \( m, n \in \mathbb{N} \) is divided by 8 is
For all \( n \in \mathbb{N} \), if \( 1^3 + 2^3 + 3^3 + \cdots + n^3>x \), then a value of \( x \) among the following is:
If \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ l & m & n \end{bmatrix} \] is a matrix such that $|A|>0$ and \[ Adj(A) = \begin{bmatrix} 0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4 \end{bmatrix}, \] then find the value of \[ \frac{cd}{fb} + \frac{ln}{em}. \]
If \[ A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix} \] and \( A^T \) represents the transpose of \( A \), then calculate \( AA^T - A - A^T \).
If the system of equations \( 2x + py + 6z = 8 \), \( x + 2y + qz = 5 \) and \( x + y + 3z = 4 \) has infinitely many solutions, then \( p = \)?
Evaluate \[ \frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + .s \text{ up to } 24 \text{ terms}. \]
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$