Tag: applications of matrices and determinants
Questions Related to applications of matrices and determinants
Inverse of $\begin{bmatrix} -1 & 5 \ -3 & 2 \end{bmatrix}$ is
Consider three matrices $A=\begin{bmatrix} 2 & 1 \ 4 & 1 \end{bmatrix}, B=\begin{bmatrix} 3 & 4 \ 2 & 3 \end{bmatrix}$ and $C=\begin{bmatrix} 3 & -4 \ -2 & 3 \end{bmatrix}$. Then the value of the sum $tr(A)+tr\left(\dfrac{ABC}{2}\right)+tr\left(\dfrac{A(BC)^{2}}{4}\right)+tr\left(\dfrac{A(BC)^{3}}{8}\right)+....+\infty$ is
If A is a 2 X 2 matrix such that $A^2009 + A^2008$= I, then : $(A^2008)^-1$=
If $I=I=\left[ \begin{matrix} 1 \ 0 \end{matrix}\begin{matrix} 0 \ 1 \end{matrix} \right] ,j=\left[ \begin{matrix} 0 \ -1 \end{matrix}\begin{matrix} 1 \ 0 \end{matrix} \right] and B=\left[ \begin{matrix} cos\theta \ -sin\theta \end{matrix}\begin{matrix} sin\theta \ cos\theta \end{matrix} \right] ,$ then B =
If $A(\theta) = \begin{bmatrix}\sin \theta & i \cos \theta\ i \cos \theta & \sin \theta\end{bmatrix}$, then which of the following is not true?
Write the following transformation in matrix form
$\quad x _1 = \displaystyle\frac{\sqrt 3}{2}y _1 + \displaystyle\frac{1}{2}y _2; \quad x _2 = -\displaystyle\frac{1}{2}y _1 + \displaystyle\frac{\sqrt 3}{2}y _2$.
Hence find the transformation in matrix form which expresses $y _1, y _2$ in terms of $x _1, x _2$.
Let p be a non-singular matrix, $1+p+p^{2}+....+p^{n}=0$ (0 denotes the null matrix) then $p^{-1}=$
Let A be a $3 \times 3$ matrix such that is: $A\left[ \begin{matrix} 1 & 2 & 3 \ 0 & 2 & 3 \ 0 & 1 & 1 \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \end{matrix} \right] $Then $A^{-1}$ is
Use the method of elementary row transformation to compute the inverse of
$\quad \begin{bmatrix} 1 & 2 & 5 \ 2 & 3 & 1 \ -1 & 1 & 1\end{bmatrix}$
If $
A=\left[ \begin{array}{ll}{x} & {1} \ {1} & {0}\end{array}\right]
$ and $
A^{2}=I
$, $
A^{-1}
$ is equal to ...............