Recent questions tagged sec-c

if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} ,$ prove that $ A^3 - 6A^2 + 7A + 2I = 0 $

asked Nov 25, 2012 by pady_1

1 answer

Find the equation of the tangent to the curve $y = \sqrt {3x - 2}$ which is parallel to the line $4x - 2y + 5 = 0 $.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

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

asked Nov 23, 2012 by pady_1

1 answer

if $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$ prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix} , n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

If $A$ and $B$ are square matrices of the same order such that $AB = BA $, then prove by induction that $AB^n = B^nA $. Further, prove that $ (AB)^n = A^nB^n \: $ for all $ n ∈ N. $

asked Nov 22, 2012 by pady_1

1 answer

Differentiate w.r.t. $x$ the function in $ x^{\large x^2-3} + ( x - 3 )^{\large x^2} $, for $x > 3$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ sin^3x + cos^6x $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If $x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} $, show that $\frac {\large dy}{\large dx} = -\frac{\large y}{\large x} $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \large\frac{\sin^3t}{\sqrt {\cos 2t}}, $$y = \large\frac{\cos^3t}{\sqrt {\cos 2t}} $ without eliminating the parameter, Find $\large\frac{ dy}{ dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the functions given in $ x^{\large y }+ y^{\large x }= 1 $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x \cos x )^{\large x} + (x\sin x)^{\Large\frac{1}{x}} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x \cos x} + \large\frac{x^2 + 1}{x^2 - 1} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x ^{\large\sin x} + (\sin x)^{\large\cos x} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x$ : $ (\sin x )^{\large x} + \sin^{-1} \sqrt x $

asked Nov 17, 2012 by thanvigandhi_1

1 answer