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Recent questions tagged p57

If $\begin{bmatrix}xy & 4\\z+6 & x+y\end{bmatrix}=\begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}$ then find the value of x,y,z and w

asked Mar 7, 2013 by sreemathi.v

1 answer

Find inverse,by elementary row operations(if possible),of the following matrices$(ii)\quad\begin{bmatrix}1 &- 3\\-2 & 6\end{bmatrix}$

asked Mar 7, 2013 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

Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;,\;a=4,b=-2\;$.Show that:$\;(c)\;(a+b)B=aB+bB$

asked Dec 23, 2012 by sreemathi.v

1 answer

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