Recent questions in Matrices

If $A=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},$ then $A^2$ is equal to

asked Dec 23, 2012 by sreemathi.v

1 answer

If A and B are two matrices of the order $3\times m\;and\;3\times n,$ respectively,and m=n,then the order of matrix(5A-2B) is

asked Dec 23, 2012 by sreemathi.v

1 answer

If $\begin{bmatrix}2x + y & 4x\\5x - 7 & 4x\end{bmatrix}=\begin{bmatrix}7 & 7y - 13\\y & x + 6\end{bmatrix},$ then the value of x,y is

asked Dec 23, 2012 by sreemathi.v

1 answer

Total number of possible matrices of order $3\times 3$ with each entry 2 or 0 is

asked Dec 23, 2012 by sreemathi.v

1 answer

The matrix $P=\begin{bmatrix}0 & 0 & 4\\0 & 4 & 0\\4 & 0 & 0\end{bmatrix}$ is a

asked Dec 23, 2012 by sreemathi.v

1 answer

Express the matrix $\begin{bmatrix}2 & 3 & 1\\1 & -1 & 2\\4 & 1 & 2\end{bmatrix}\;$ as the sum of symmetric and skew symmetric matrices P&Q.

asked Dec 23, 2012 by sreemathi.v

1 answer

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

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

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

asked Dec 22, 2012 by sreemathi.v

1 answer

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

asked Dec 22, 2012 by sreemathi.v

1 answer

Show that if A and B are square matrices such that AB=BA,then $(A+B)^2=A^2+2AB+B^2$

asked Dec 22, 2012 by sreemathi.v

1 answer

Let A and B be the square matrices of the order $3\times 3$ .Is $(AB)^2=A^2B^2?$ Give reasons

asked Dec 22, 2012 by sreemathi.v

1 answer

Show that $A'A$ and $AA'$ are both symmetric matrices for any matrix A

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(i)\quad(2A+B)'=2A'+B'$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(i)\quad(A')'=A$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 0 & -1\\2 & 1 & 3\\0 & 1 & 1\end{bmatrix},then\;verify\;that\;A^2+A=A(A+I),where\;I\;is\;3\times 3\;unit\;matrix.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}2 & 1\end{bmatrix}\;B=\begin{bmatrix}5 & 3 & 4\\8 & 7 & 6\end{bmatrix}\;andC=\begin{bmatrix}-1 & 2 & 1\\1 & 0 & 2\end{bmatrix},verify\;that\;A(B+C)=(AB+AC)$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $\begin{bmatrix}2 & 1 & 3\end{bmatrix}\begin{bmatrix}-1 & 0 & -1\\-1 & 1 & 0\\0 & 1 & 1\end{bmatrix}\begin{bmatrix}1\\0\\-1\end{bmatrix}=A,find\;A.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $P=\begin{bmatrix}x & 0 &0\\0 & y & 0\\0 & 0 & z\end{bmatrix}\;$ and $\;Q=\begin{bmatrix}a & 0 & 0\\0 & b & 0\\0 & 0 & c\end{bmatrix}$ prove that $PQ=\begin{bmatrix}xa & 0 & 0\\0 & yb & 0\\0 & 0 & zc\end{bmatrix}=QP$

asked Dec 22, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(i)\;(AB)C=A(BC)$

asked Dec 22, 2012 by sreemathi.v

1 answer

Which of the following is an example of matrices A,B and C such that AB=AC,where A is non-zero matrix,but $B\neq C.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If A=[3 , 5],B=[7, 3],then find a non-zero matrix C such that AC=BC.

asked Dec 22, 2012 by sreemathi.v

1 answer

If X and Y are $2\times 2$ matrices,then solve the following matrix equation for X and Y $2X+3Y=\begin{bmatrix}2 & 3\\4 & 0\end{bmatrix},3X+2Y=\begin{bmatrix}-2 & 2\\1 & -5\end{bmatrix}.$

asked Dec 22, 2012 by sreemathi.v

1 answer

Solve for x and y: $x\begin{bmatrix}2\\1\end{bmatrix}+y\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$

asked Dec 22, 2012 by sreemathi.v

1 answer

Given $A=\begin{bmatrix}2 & 4 & 0\\3 & 9 & 6\end{bmatrix}\;and\;B=\begin{bmatrix}1& 4\\2 & 8\\1 & 3\end{bmatrix}.\;Is \;(AB)'=B'A'?$

asked Dec 22, 2012 by sreemathi.v

1 answer

Show by an example that for $A\neq 0,B\neq 0,AB=0.$

asked Dec 22, 2012 by sreemathi.v

1 answer

If possible,find BA and AB,where $A=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix},B=\begin{bmatrix}4 & 1\\2 & 3\\1 & 2\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

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