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Questions >> JEEMAIN and NEET >> Mathematics >> Class12 >> Matrices

Let $M$ and $N$ be two $3\times 3$ non singular skew-symmetric matrices such that $MN=NM$ .If PT denotes the transpose of P,then $M^2N^2(M^TN)^{-1}(MN^{-1})^T$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

If $P$ is a $3\times 3$ matrix such that $P^T=2P+1$ where $P^T$ is the transpose of $p$ and $I$ is the $3\times 3$ identity matrix then there exists a column matrix $x=\begin{bmatrix}x\\y\\z\end{bmatrix}\neq \begin{bmatrix}0\\0\\0\end{bmatrix}$ such that

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $\omega\neq 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form $\begin{vmatrix}1&a&b\\\omega&1&c\\\omega^2&\omega&1\end{vmatrix}$ where each of a,b and c is either $\omega$ or $\omega^2$ .Then the number of distinct matrices in the set S is

asked Nov 20, 2013 by sreemathi.v

1 answer

The number of $3\times 3$ matrices A whose entries are either 0 or 1 and for which the system $A=\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$ has exactly two distinct solution is

asked Nov 20, 2013 by sreemathi.v

1 answer

If $A=\begin{vmatrix}\alpha &0\\1 &1\end{vmatrix}$ and $B=\begin{vmatrix}1 &0\\5 &1\end{vmatrix}$ then the value of $\alpha$ for which $A^2=B$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}1 &x&x+1\\2x&x(x-1)&(x+1)x\\3x(x-1)&x(x-1)(x-2)&(x+1)x(x-1)\end{vmatrix}$ then $f(100)$ is equal to

asked Nov 20, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of equal degree,then which one is correct among the following

asked Nov 20, 2013 by sreemathi.v

1 answer

If $\omega(\neq 1)$ is a cube root of unity,then $\begin{vmatrix}1 &1+i+\omega^2&\omega^2\\1-i&-1&\omega^2-1\\-i&-i+\omega-1&-1\end{vmatrix}$ =

asked Nov 20, 2013 by sreemathi.v

1 answer

Given that $x=-9$ is a root of $\begin{vmatrix}x&3&7\\2 &x&2\\7&6&x\end{vmatrix}$ = 0, the other two roots are

asked Nov 20, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}1 &-\tan\theta\\\tan\theta&1\end{bmatrix}\begin{bmatrix}1 &\tan\theta\\-\tan\theta&1\end{bmatrix}^{-1}$ = $\begin{bmatrix}a &-b\\b&a\end{bmatrix}$ then find $a,b$

asked Nov 19, 2013 by sreemathi.v

1 answer

Find the product of the matrices $\begin{bmatrix}2 &3&4\\-1&2&-5\end{bmatrix}$ and $\begin{bmatrix}1&2\\3&-4\\-5&6\end{bmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

Given matrices $A=\begin{bmatrix}5 &-2&0\\3&0&5\\-1&0&8\end{bmatrix}$ , $B=\begin{bmatrix}0 &-2\\1 &0\\0&5\end{bmatrix}$ , find $(A+B)$ .

asked Nov 19, 2013 by sreemathi.v

1 answer

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