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Recent questions tagged easy

If A and B are square matrices of the same order,then $\quad (AB)'=\text{________}.$

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is a skew symmetric matrix, then $A^2$ is a ____________ .

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is a symmetric matrix, then $A^3$ is a _________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

Matrix multiplication is __________ over addition.

asked Dec 24, 2012 by sreemathi.v

1 answer

A matrix which is not a square matrix is called a __________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

The product of any matrix by the scalar ____________ is the null matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

Sum of two skew symmetric matrices is always ____________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

________________ matrix is both symmetric and skew symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

On using elementary row operations $R_2\times R_1-3R_2$ in the following matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$,we have:

asked Dec 24, 2012 by sreemathi.v

1 answer

On using elementary column operations $C_2\times C_2-2C_1$ in the following matrix equation\[\begin{bmatrix}1 & 3\\2 & 4\end{bmatrix}=\begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}\begin{bmatrix}3 & 1\\2 & 4\end{bmatrix}, \text{we have}\]

asked Dec 24, 2012 by sreemathi.v

1 answer

For any two matrices A and B,we have

asked Dec 24, 2012 by sreemathi.v

1 answer

If A and B are matrices of same order ,then (AB'-BA') is a

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is matrix of order $m\times n$ and B is a matrix such that AB' and B'A are both defined,then order of matrix B is

asked Dec 24, 2012 by sreemathi.v

1 answer

The matrix $\begin{bmatrix}0 & 5 & 8\\5 & 0 & 12\\8 & 12 & 0\end{bmatrix}$ is

asked Dec 24, 2012 by sreemathi.v

1 answer

The matrix $\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$ is a

asked Dec 23, 2012 by sreemathi.v

1 answer

If Matrix $A=[a_{ij}]_{2\times 3},$ where$a_{ij} \begin{array}{ 1 1}=1\;if\;i\neq j\\=0\;if\;i=j\end{array}$ then $\;A^2\;$ is equal to:

asked Dec 23, 2012 by sreemathi.v

1 answer

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

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

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

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

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

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

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

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