Recent questions and answers in Matrices

If $ A=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix},\;then\;A^5=?$

answered Dec 25, 2018 by awokekefale2018

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If $ A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$ find x and y such that $ A^2+xl=yA.\;Find\;A^{-1}.$

answered Jun 20, 2018 by vasuloki708

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Find the value of $x, y, z $ if the matrix. $\begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfy the equation $A^TA =I_3$

answered Dec 21, 2016 by priyanka.c

1 answer

If $A =\begin{bmatrix} x & -2 \\ 3 & 7 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} \frac{7}{34} & \frac{1}{17} \\ \frac{3}{34} & \frac{2}{17} \end{bmatrix}$ then find the value of $x $.

answered Dec 20, 2016 by priyanka.c

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For what value of $\lambda$, the matrix $\begin{bmatrix} 1 & \lambda & 0 \\ 3 & -1 & 2 \\ 4 & 1 & 5 \end{bmatrix} $ is singular ?

answered Dec 20, 2016 by priyanka.c

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Three shopkeepers X,Y and Z go to a store to buy stationery items. X purchases 12 dozen marker pens, 5 dozen ink pen and 6 dozen pencils. Y purchases 10 dozen marker pens, 6 dozen ink pen and 7 dozen pencils. Z purchases 11 dozen marker pens, 13 dozen ink pens and 8 dozen pencils. A marker pen cost Rs 40/- , a pen costs Rs. 7/- and a pencil Rs. 1 /- each. Using matrix multiplication calculate the individual bills of X, Y and Z.

answered Dec 9, 2016 by priyanka.c

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For what values of $x$ and $y$ are the following matrices equal ? $A = \begin{bmatrix} 2x+1 & 3y \\ 0 & y^2-5y \end{bmatrix} , B = \begin{bmatrix} x+3 & y^2+2 \\ 0 &-6 \end{bmatrix}$

answered Dec 8, 2016 by priyanka.c

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If A and B are symmetric matrices, prove that AB - BA is a skew symmetric matrix

answered Dec 6, 2016 by priyanka.c

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If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix} $ , Evaluate $A^TA^{-1}$

answered Dec 1, 2016 by priyanka.c

1 answer

Find the value of x if $\begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2& 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0$

answered Nov 23, 2016 by priyanka.c

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Evalute : $\begin{vmatrix}152 & 24 & 40 \\ 3 & 7 & 1 \\ 19 & 3 & 5 \end{vmatrix}$

answered Nov 23, 2016 by priyanka.c

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Use matrix method to examine if the following system of equation for consistency or inconsistency $4x - 2y = 3, \; \; 6x - 3y = 5$

answered Nov 22, 2016 by priyanka.c

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Without expanding evaluate: $\begin{vmatrix} \frac{1}{a} & a^2 & bc \\ \frac{1}{b} & b^2 & ca \\ \frac{1}{c} & c^2 & ab \end{vmatrix}$

answered Nov 22, 2016 by priyanka.c

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Using elementary row transformation, find the inverse of $A = \begin{bmatrix} 2 & -6 \\ 1 & -2\end{bmatrix}$

answered Nov 21, 2016 by priyanka.c

1 answer

Solve the system of equation $2x + 5y = 1 \; \ \; \; and \; \; \; \; 3x + 2y = 7$

answered Nov 20, 2016 by priyanka.c

1 answer

Find X and Y, if $X + Y= \begin{bmatrix} 5 & 2 \\ 0 & 9 \end{bmatrix}$ and $X - Y = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$

answered Nov 20, 2016 by priyanka.c

1 answer

If $ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then find the value of $\theta$ satisfying the equation $A^T + A = I_2$

answered Nov 20, 2016 by priyanka.c

1 answer

Find the equation of the line joining (1,3) and B (0, 0) using determinants and find K if D (K,0) is a point such that area of $\triangle ABD$ is 3 sq. units

answered Nov 18, 2016 by priyanka.c

1 answer

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

answered Nov 17, 2016 by priyanka.c

1 answer

If $\begin{pmatrix} a+4 &3b \\ 8 & -6 \end{pmatrix} = \begin{pmatrix} 2a+2 &b+2 \\ 8 & a-8b \end{pmatrix}$, write the value of $a-2b$.

answered Mar 21, 2014 by balaji.thirumalai

1 answer

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is?

asked Feb 18, 2014 by balaji.thirumalai

1 answer

If $A=\begin{bmatrix}2 & sec^{-1}x\\-1 & cosec^{-1} x \end{bmatrix}$ is a singular matrix then find the value of $x$

answered Feb 6, 2014 by rvidyagovindarajan_1

1 answer

If $A=\begin{bmatrix}2 & 3\\5 & -2\end{bmatrix}$ then express $A^{-1}$ in terms of $A$

answered Jan 30, 2014 by rvidyagovindarajan_1

1 answer

Given $A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ How can we express $A^{-1}$ in terms of A?

answered Jan 29, 2014 by balaji

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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.

answered Jul 17, 2013 by sharmaaparna1

1 answer

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

answered Jul 17, 2013 by sharmaaparna1

1 answer

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

answered Jul 13, 2013 by sharmaaparna1

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

answered Jul 13, 2013 by sharmaaparna1

1 answer

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

answered Jul 13, 2013 by sharmaaparna1

1 answer

If A=$\begin{bmatrix}1 & 2& 2\\2 & 1 & 2\\2 & 2&1\end{bmatrix}$ verify that $A^2-4A-5I=0.$

answered Jul 12, 2013 by sharmaaparna1

1 answer

Using elementary transformations, find the inverse of the following matrix : $ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5 \end{bmatrix} $

answered Apr 6, 2013 by sharmaaparna1

1 answer

True or False: If $A =\begin{bmatrix} 2 & 3 & 1 \\ 1 &4 & 2 \end{bmatrix}\; and\; B=\begin{bmatrix}2 & 3 \\ 4& 5 \\ 2 & 1 \end{bmatrix},$ then AB and BA are defined and equal.

answered Apr 5, 2013 by sharmaaparna1

1 answer

The number of all possible matrices of order $2\times 2$ with each entry 0 & 1.\[(A)\;27 \quad(B)\;18\quad(C)\;81\quad(D)\;16\]

answered Apr 4, 2013 by sreemathi.v

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If A and B are skew symmetric matrices,then prove that ABA is skew symmetric.

answered Apr 4, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}3 & 1\\7 & 5\end{bmatrix}$ find x & y such that $A^2+xI=yA$

answered Apr 4, 2013 by sreemathi.v

1 answer

If A=$\begin{bmatrix}3 & 2\\1 & 1\end{bmatrix}$ find the values of a and b, such that $A^2+aA+bI=0.$

answered Apr 4, 2013 by sreemathi.v

1 answer

Find $A^{-1}$ if it exists by using elementary transformations where A=$\begin{bmatrix}6 & -3\\-2 & 1\end{bmatrix}$

answered Apr 4, 2013 by sreemathi.v

1 answer

Find the inverse of the following matrices if it exists using elementary operations $\begin{bmatrix}2 & -6\\1 & -2\end{bmatrix}$

answered Apr 4, 2013 by sreemathi.v

1 answer

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

answered Apr 4, 2013 by sharmaaparna1

1 answer

If A and B are square matrices of the same order,then $(ii)\quad (kA)'=\text{________}.$(k is any scalar)

answered Apr 4, 2013 by sharmaaparna1

1 answer

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

answered Apr 4, 2013 by sharmaaparna1

1 answer

Find the inverse of the following matrices if it exists using elementary operations $\begin{bmatrix}2 & 5\\1 & 3\end{bmatrix}$

answered Apr 4, 2013 by sreemathi.v

1 answer

Find the transpose of the matrix $\begin{bmatrix}1 & 3\\2 & 6\\5 & -3\end{bmatrix}$

answered Apr 4, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & -1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}2 & 1\\1 & 0\end{bmatrix}$ prove that $(A+B)^2\neq A^2+2AB+B^2$

answered Apr 4, 2013 by sreemathi.v

1 answer

If A and B are symmetric matrices,then $\quad AB-BA\;is\;a\;\text{_______}$

answered Apr 4, 2013 by sharmaaparna1

1 answer

If A and B are symmetric matrices,then $(ii)\quad BA-2AB\;is\;a\;\text{_______}$

answered Apr 4, 2013 by sharmaaparna1

1 answer

If $A=\begin{bmatrix}0 & 1\\0 &0\end{bmatrix}$ prove that for all $n\in N.(aI+bA)^n=a^nI+na^{n-1}bA.$where I is the identity matrix of order 2.

answered Apr 4, 2013 by sreemathi.v

1 answer

If A=$\begin{bmatrix}cos\theta & -sin\theta\\sin\theta & cos\theta\end{bmatrix}$.Then show that $A^n=\begin{bmatrix}cos n \theta&-sin n\theta\\sin n\theta & cos n\theta\end{bmatrix}$where n is a positive integer.

answered Apr 4, 2013 by sreemathi.v

1 answer

Find matrix X if $X+\begin{bmatrix}2 & 5\\3 & -1\end{bmatrix}=\begin{bmatrix}3 & 4\\2 & 0\end{bmatrix}$

answered Apr 4, 2013 by sreemathi.v

1 answer

Use product of AB where $A= \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} \; and \;B=\begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix}$ <br> to solve the system of equations : $ \\ x-y+2z=1 \\ 2y-3z=1 \\ 3x-2y+4z=2 $

answered Apr 4, 2013 by meena.p

1 answer

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