Recent questions tagged ch3

If possible,using elementary row transformations,find the inverse of the following matrices $\quad\begin{bmatrix}2 & -1 & 3\\-5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked Dec 23, 2012 by sreemathi.v

1 answer

Find x,y,z if $A=\begin{bmatrix}0 & 2y & z\\x & y & -z\\x & -y & z\end{bmatrix}\;satisfies\;A'=A^{-1}$.

asked Dec 23, 2012 by sreemathi.v

1 answer

If AB=BA for any two square matrices,prove by mathematical induction that $(AB)^n=A^nB^n$.

asked Dec 23, 2012 by sreemathi.v

1 answer

If A,B are square matrices of same order and B is a skew-symmetric matrix,show that A'BA is skew symmetric.

asked Dec 23, 2012 by sreemathi.v

1 answer

If A is square matrix such that $A^2=A,$show that $(I+A)^3=7A+I.$

asked Dec 23, 2012 by sreemathi.v

1 answer

If $P(x)=\begin{bmatrix}\cos x & \sin x\\-\sin x & \cos x\end{bmatrix}$,then show that\[P(x).P(y)=P(x+y)=P(y).P(x).\]

asked Dec 23, 2012 by sreemathi.v

1 answer

Find the value of $\alpha$ if $A=\begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$ and $\;A^{-1}=A'$

asked Dec 23, 2012 by sreemathi.v

1 answer

If the matrix $\begin{bmatrix}0 & a & 3\\2 & b & -1\\c & 1 & 0\end{bmatrix}\;$is a skew symmetric matrix,find the values of a,b and c.

asked Dec 23, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\4 & 1\end{bmatrix},find\;A^2+2A+7I.$

asked Dec 23, 2012 by sreemathi.v

1 answer

Find the matrix A such that$\begin{bmatrix}2 & -1\\1 & 0\\-3 & 4\end{bmatrix}\;A=\begin{bmatrix}-1 & -8 & -10\\1& -2 & -5\\9 & 22 &15\end{bmatrix}.$

asked Dec 23, 2012 by sreemathi.v

1 answer

Find the values of a,b,c and d,if $3\begin{bmatrix}a & b\\c & d\end{bmatrix}=\begin{bmatrix}a & 6\\-1 & 2d\end{bmatrix}+\begin{bmatrix}4 & a+b\\c+d & 3\end{bmatrix}$

asked Dec 23, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3 & -5\\-4 & 2\end{bmatrix},$ then find $A^2-5A-14I.$Hence,obtain $A^3$.

asked Dec 23, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 5\\7 & 12\end{bmatrix}\;and\;B=\begin{bmatrix}9 & 1\\7 & 8\end{bmatrix},$ find a matrix $C$ such that $3A+5B+2C$ is a null matrix.

asked Dec 23, 2012 by sreemathi.v

1 answer

Find inverse,by elementary row operations(if possible),of the following matrices$\quad\begin{bmatrix}1 & 3\\-5 & 7\end{bmatrix}$

asked Dec 23, 2012 by sreemathi.v

1 answer

Prove by Mathematical Induction that $(A')^n=(A^n)'$,where $n\in N$ for any square matrix A.

asked Dec 23, 2012 by sreemathi.v

1 answer

Verify that $A^2=I\;when\;A=\begin{bmatrix}0 & 1 & 1\\4 & 3 & 4\\3 & 3 & 4\end{bmatrix}.$

asked Dec 23, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0 & x\\x & 0\end{bmatrix},B=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\;and\;x^2=-1,then\;show\;that\;(A+B)^2=A^2+B^2.$

asked Dec 23, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{bmatrix},\;then\;show\;that\;A^2=\begin{bmatrix}\cos2\theta & \sin2\theta\\-\sin2\theta & \cos2\theta\end{bmatrix}.$

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(i)\;(A-B)^T=A^T-B^T.\]

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(h)\;(A-B)C=AC-BC.\]

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;$and$\;a=4,b=-2$.Show that$\;(g)\;(AB)^T=B^TA^T.$

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(f)\;(bA)^T=bA^T.\]

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(e)\;(A^T)^T=A.\]

asked Dec 23, 2012 by sreemathi.v

1 answer

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(d)\;a(C-A)=aC-aA.\]

asked Dec 23, 2012 by sreemathi.v

1 answer