Recent questions tagged operations-on-matrices

$\begin{vmatrix}\log_3512&\log_43\\\log_38&\log_49\end{vmatrix}\times \begin{vmatrix}\log_23&\log_83\\\log_34&\log_34\end{vmatrix}=$

asked Apr 24, 2014 by sreemathi.v

1 answer

Let $C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$ be a $2\times 2$ matrix and there exist $2\times 2$ matrices $A$ and $B$ such that $C=AB-BA$ then

asked Apr 24, 2014 by sreemathi.v

1 answer

If $a=1+2+4+.........$upto n terms,$b=1+3+9+.....$upto n terms,$c=1+5+25+.....$upto n terms then $\begin{vmatrix}a&2b&4c\\2&2&2\\2^n&3^n&5^n\end{vmatrix}=$

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$ and $kA=\begin{bmatrix}0&3a\\2b&24\end{bmatrix}$ then the values of $k,a,b$ are respectively

asked Apr 23, 2014 by sreemathi.v

1 answer

For each real numbers $x$ such that $-1 < x < 1$ let $A(x)$ be the matrix.$(1-x)^{-\large\frac{1}{2}}\begin{bmatrix}1&-x\\-x&1\end{bmatrix}$ and $z=\large\frac{x+y}{1+xy}$.Then

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&1&0\\0&0&1\\1&-1&0\end{bmatrix}$ then $A^3+A$ equals

asked Apr 23, 2014 by sreemathi.v

1 answer

If $S_r=\begin{vmatrix}2r&x&n(n+1)\\6r^2-1&y&n^2(2n+3)\\4r^32nr&z&n^3(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n S_r$ is independent of

asked Apr 22, 2014 by sreemathi.v

1 answer

Matrix $A$ satisfies $A^2=2A-I$ where $I$ is the identity matrix. For $n \geq 2$, $A^n$ is equal to $(n\in N)$

asked Nov 25, 2013 by sreemathi.v

1 answer

If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $xyz$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}0&a\\b&0\end{bmatrix}^4=I$ then

asked Nov 25, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$ then $A^4$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

The value of $\begin{vmatrix}x&p&q\\p&x&q\\p&q&x\end{vmatrix}$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

If the matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\0&1\end{bmatrix}$ then

asked Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1&-2\\4&5\end{bmatrix}$ and $f(1)=t^2-3t+7$ then $f(A)+\begin{bmatrix}3&6\\-12&-9\end{bmatrix}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $\begin{bmatrix}2&1\\3&2\end{bmatrix}A\begin{bmatrix}-3&2\\5&-3\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ then the matrix A is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}a&b\\b&a\end{bmatrix}$ and $A^2=\begin{bmatrix}\alpha&\beta\\\beta&\alpha\end{bmatrix}$ then

asked Nov 21, 2013 by sreemathi.v

1 answer

Let $\omega$ be a complex cube root of unity with $\omega\neq 1$ and $p=[P_{ij}]$ be a $n\times n$ matrix with $P_{ij}=\omega^{i+j}$.Then $P^2\neq 0$ when $n$=

asked Nov 21, 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

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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