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Recent questions tagged p142

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(ii)\big(A^{-1}\big)^{-1}$

asked Mar 1, 2013 by sreemathi.v

1 answer

The least value of the function $f(x)=ax+\frac{b}{x}(a>0,b>0,x>0)$ is ___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=\Large\frac{2x^2-1}{x^4}$,x>0,decreases in the interval__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The value of a for which the function $f(x)=sin x-ax+b$ increases on R are__________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The equation of normal to the curve y=tan x at (0,0) is___________.

asked Jan 12, 2013 by sreemathi.v

1 answer

The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point_________.

asked Jan 12, 2013 by sreemathi.v

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} 3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{bmatrix} = 3(a + b + c)(ab+bc+ca) $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} sin\alpha&cos\alpha&cos(\alpha+\delta)\\ sin\beta&cos\beta&cos(\beta+\delta)\\ sin\gamma&cos\gamma&cos(\gamma+\delta)) \end{vmatrix}= 0.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 1&1+p&1+p+q\\ 2&3+2p&4+3p+2q\\ 3&6+3p&10+6p+3q \end{vmatrix}= 1.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $ \begin{vmatrix} x &x^2 &1 & px^3\\ y &y^2 &1 & py^3\\ z &z^2 &1 & pz^3 \end{vmatrix}= (1+pxyz) (x-z) (y-z)(z-x), $ where p is any scalar.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} \alpha & \alpha^2 & \beta+\gamma\\ \beta & \beta^2 & \alpha+\gamma\\ \gamma & \gamma^2 & \alpha+\beta \end{vmatrix} = (\beta-\gamma) (\gamma - \alpha) (\alpha-\beta) (\alpha+\beta+\gamma)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\ 1 & x & x+y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} x & y & x+y\\ y & x+y & x\\ x+y & x & y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(i)\ \; \left [adj A \right ]^{-1} = adj(A^{-1}) \;\;\;\; $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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