Recent questions tagged sec-b

Show that $A=\begin{bmatrix} xc_{r} & xc_{r+1} & xc_{r+2} \\ yc_r & yc_{r+1} & yc_{r+2} \\ zc_r & zc_{r+1} & zc_{r+2} \end{bmatrix}=\begin{bmatrix} xc_{r} & x+1c_{r+1} & x+2c_{r+2} \\ yc_r & y+1c_{r+1} & y+2c_{r+2} \\ zc_r & z+1c_{r+1} & z+2c_{r+2} \end{bmatrix}$

asked Apr 5, 2013 by meena.p

1 answer

Show that the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are coplanar if and only if $\overrightarrow{a}+\overrightarrow{b},\overrightarrow{b}+\overrightarrow{c},\overrightarrow{c}+\overrightarrow{a}$ are coplanar.

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove that $\begin{vmatrix} (x-2)^2 & (x-1)^2 & x^2 \\ (x-1)^2 & x^2 & (x+1)^2 \\ x^2 & (x+1)^2 & (x+2)^2 \end{vmatrix}=-8$

asked Apr 5, 2013 by meena.p

1 answer

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

asked Apr 4, 2013 by sreemathi.v

1 answer

Evaluate $\left|\begin{array}{ccc} 1 & \omega^n & \omega^{2n} \\ \omega^{2n} & 1 & \omega^{n} \\ \omega^n & \omega^{2n} & 1 \end{array}\right|$

asked Apr 4, 2013 by meena.p

1 answer

Without expanding evaluate the determinent $\begin{vmatrix} (a^x+a^{-x})^2 & (a^x-a^{-x})^2 & 1 \\ (a^y+a^{-y})^2 & (a^y-a^{-y})^2 & 1 \\ (a^z+a^{-z})^2 & (a^z-a^{-z})^2 & 1 \end{vmatrix}$ where $a>0$ ,and $x,y,z \in R$

asked Apr 3, 2013 by meena.p

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x-4y+7z=14\;,3x+8y-2z=13\;,7x-8y+26z=5 $

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6 $

asked Mar 30, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $3x+y-z=2\;,2x-y+2z=6\;,2x+y-2z=-2 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $3x+2y=5\;,x+3y=4$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 0 & 1 & 2 &1 \\2 & -3 & 0 &-1 \\1 & 1 & -1 & 0 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 3 & 1 & 2 &0 \\1 & 0 & -1 &0 \\2 & 1 & 3 &0 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & 1 & -1 \\3 & -2 & 3 \\2 & -3 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;7x\;+\;3y\;=\;-1\;,\;2x\;+\;y\;=\;0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation:$\;2x\;-\;y\;=7\;,\;3x\;-2y\;=11$

asked Mar 29, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that$(AB)^{T}=B^{T}A^{T}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the inverse of following matrix: $\begin{bmatrix} 1 & 3 & 7 \\4 & 2 & 3 \\1 & 2 & 1 \end{bmatrix}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the inverse of following matrix :$\begin{bmatrix} 1 & 0 & 3 \\2 & 1 & -1 \\1 & -1 & 1 \end{bmatrix}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the adjoint of the matrix A =$\begin{bmatrix} 1 & 2 \\3 & -5 \end{bmatrix}$ and verify the result $ A\;(adj\; A)=(adj\;A)\;A=$|$A$|$.I$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the adjoint of the following matrics;$\begin{bmatrix} 2& 5 & 3 \\3 & 1 & 2 \\1 & 2 & 1 \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

Find the adjoint of the following matrices:$\begin{bmatrix} 1 & 2 & 3 \\0 & 5 & 0 \\2 & 4 & 3 \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

Using properties of determinants,prove the following $\begin{vmatrix}3x& -x+y & -x+z\\x-y & 3y & z-y\\x-z & y-z & 3z\end{vmatrix}=3(x+y+z)(xy+yz+zx)$

asked Mar 22, 2013 by sreemathi.v

1 answer

If $x\sin (a+y)+\sin a \cos(a+y)=0$,Prove that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^3+1)}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Using vectors,find the area of triangle ABC,whose vertices are $A(1,2,3),B(2,-1,4),C(4,5,-1).$

asked Mar 22, 2013 by sreemathi.v

1 answer

Using the property of determinants, evalute: $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

What is the value of $tan\bigg(\frac{1}{2}sin^{-1}\frac{3}{4}\bigg)$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

If $\overrightarrow{p}=5\hat{i}+\lambda\hat{j}-37\hat{k}$ and $\overrightarrow{q}=\hat{i}+3\hat{j}-5\hat{k}$,then find the value of $\lambda$,so that $\overrightarrow{p}+\overrightarrow{q}$ and $\overrightarrow{p}-\overrightarrow{q}$ are perpendicular vectors.

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int\limits_0^{\pi}\large\frac{xsin x}{1+cos^2x}dx.$

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^3+8)}$

asked Mar 22, 2013 by sreemathi.v

1 answer