Recent questions tagged medium

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the adjoint of the matrix: $\begin{bmatrix} 1&-1&2 \\ 2&3&5 \\ -2&0&1 \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the particular solution of the differential equation $(1+e^{2x})dy + (1+y^2)e^xdx$ = 0, given that $y = 1$ when $x = 0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution of the differential equation $(x-y)(dx+dy) = dx - dy$,given that $ y=\;-1$,when $ x=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the differential equation $\begin{bmatrix}\large\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\large\frac{y}{\sqrt{x}}\end{bmatrix}\large\frac{dx}{dy}$$=1(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution of the differential equation $\frac{dy}{dx} + y\cot x=4x\:cosec\:x$, $(x\neq0)$, given that $y = 0$ when $x = \large\frac{\pi}{2}$

asked Nov 28, 2012 by sreemathi.v

1 answer

Choose the correct answer. If $\sin^{-1}(1-x) -2 \sin^{-1} x=\large\frac {\pi}{2}, $ then $x$ is equal to

asked Nov 28, 2012 by vaishali.a

1 answer

What is the value of: \[tan^{-1} \bigg( \frac {x}{y} \bigg) -tan^{-1} \frac {x-y}{x+y} \]

asked Nov 28, 2012 by vaishali.a

1 answer

Find equation of line joining (1, 2) and (3, 6) using determinants

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Show that the points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Solve the following $\tan^{-1} \sqrt{3} -sec^{-1} (-2)$:

asked Nov 28, 2012 by vaishali.a

2 answers

By using the properties of determinants show that $ (i) \begin{vmatrix} a-b-c&2a&2a \\ 2b&b-c-a&2b \\ 2c&2c&c-a-b \end{vmatrix} = (a+b+c)^3 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer