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Recent questions tagged p141

Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

The maximum value of $\Large\frac{1}{x}$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

$f(x)=x^x$ has a stationary point at

asked Jan 12, 2013 by sreemathi.v

1 answer

Maximum slope of the curve $y=x^3+3x^2+9x-27$ is

asked Jan 12, 2013 by sreemathi.v

1 answer

At $x=\Large\frac{5}{6}$$,f(x)=2\sin 3x+3\cos 3x$ is:

asked Jan 12, 2013 by sreemathi.v

1 answer

The maximum value of sin x,cos x is

asked Jan 12, 2013 by sreemathi.v

1 answer

The function $f(x)=2x^3-3x^2-12x+4$,has

asked Jan 12, 2013 by sreemathi.v

1 answer

The smallest value of the polynomial $x^3-18x^2+96x$ in [0,9] is

asked Jan 11, 2013 by sreemathi.v

1 answer

If x is real,the minimum value of $x^2-8x+17$ is

asked Jan 11, 2013 by sreemathi.v

1 answer

$If \; A^{-1}=\begin{bmatrix} 3 &-1 & 1\\ -15&6 &-5 \\ 5& -2&2 \end{bmatrix} \; and \; B = \begin{bmatrix} 1 & 2 & -2\\ -1 & 3 & 0\\ 0 & -2 & 1 \end{bmatrix}, \; find \; (AB)^{-1} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that $ \begin{vmatrix} a^2&bc&ac+c^2\\ a^2+ab& b^2& ac\\ ab&b^2+bc&c^2 \end{vmatrix}=4\,a^2\;b^2\;c^2. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a, b and c are real numbers, and $\Delta = \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c\\ a+b & b+c & c+a \end{vmatrix}=0, $ show that either $a+b+c=0$ or $a=b=c.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} cos\alpha \; cos\beta & cos\alpha \; sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0 \\ sin \alpha \; cos\beta & sin\alpha \; sin\beta & cos\alpha \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Without expanding the determinant, prove that $ \begin{vmatrix} a &a^2 &bc \\ b &b^2 &ca \\ c &c^2 &ab \end{vmatrix}\; = \; \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

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