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Recent questions tagged evaluate-determinants

If $ax^3+bx^2+cx+d=\begin{vmatrix}x^2&(x-1)^2&(x-2)\\(x-)^2&(x-2)^2&(x-3)^2\\(x-2)^2&(x-3)^2&(x-4)^2\end{vmatrix}$ then

asked Apr 25, 2014 by sreemathi.v

1 answer

If $1+\sin x+\cos x\neq 0$ the value of $x$ for which $\begin{vmatrix}1&\sin x&\cos x\\\sin x&1&\cos x\\\cos x&\sin x&1\end{vmatrix}=0$ is

asked Apr 25, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}\cos x&1&0\\1&2\cos x&1\\0&1&2\cos x\end{vmatrix}$ then $\int\limits_0^{\large\frac{\pi}{2}}2f(x)dx$ is equal to

asked Apr 25, 2014 by sreemathi.v

1 answer

If $A=\begin{vmatrix}a&b&c\\x&y&z\\p&q&r\end{vmatrix}$ and $B=\begin{vmatrix}q&-b&y\\-p&a&-x\\r&-c&z\end{vmatrix}$ then

asked Apr 24, 2014 by sreemathi.v

1 answer

If $D_r=\begin{vmatrix}2^{r-1}&2.3^{r-1}&4.5^{r-1}\\\alpha&\beta&\gamma\\2^n-1&3^n-1&5^n-1\end{vmatrix}$ then the value of $\sum\limits_{r=1}^n D_r$ is

asked Apr 24, 2014 by sreemathi.v

1 answer

Value of the determinant $\begin{vmatrix} 10!&11!&12!\\11!&12!&13!\\12!&13!&14!\end{vmatrix}$ is

asked Apr 24, 2014 by sreemathi.v

1 answer

If $C=2\cos \theta$ then the value of the determinant $4\Delta=\begin{vmatrix}c&1&0\\1&c&1\\0&1&c\end{vmatrix}$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If 5 is one root of the equation $\begin{vmatrix}x&3&7\\2&x&-2\\7&8&x\end{vmatrix}=0$ then the other two roots of the equation are

asked Apr 23, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}\sin x&\cos x&\tan x\\x^3&x^2&x\\2x&1&1\end{vmatrix}$ then $\lim\limits_{x\to 0}\large\frac{f(x)}{x^2}$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\omega$ is cube root of unity then $\Delta=\begin{vmatrix}x+1&\omega&\omega^2\\\omega&x+\omega^2&1\\\omega^2&1&x+\omega^2\end{vmatrix}=$

asked Apr 23, 2014 by sreemathi.v

1 answer

Suppose $D=\begin{vmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{vmatrix}$ and $D'=\begin{vmatrix}a_1+pb_1&b_1+qc_1&c_1+ra_1\\a_2+pb_2&b_2+qc_2&c_2+ra_2\\a_3+pb_3&b_3+qc_3&c_3+ra_3\end{vmatrix}$ then

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are real numbers then,$\begin{vmatrix} 1& \cos(\beta-\alpha)&\cos(\gamma-\alpha)\\\cos(\alpha-\beta)&1&\cos(\gamma-\beta)\\\cos(\alpha-\gamma)&\cos(\beta-\gamma)&1\end{vmatrix}$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta_r=\begin{vmatrix}2^{r-1}&\large\frac{(r+1)!}{1+\large\frac{1}{r}}&2r\\a&b&c\\2^n-1&(n+1)!-1&n(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n\Delta_r$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta=\begin{vmatrix} 1+x_1y_1&1+x_1y_2&1+x_1y_3\\1+x_2y_1&1+x_2y_2&1+x_2y_3\\1+x_3y_1&1+x_3y_2&1+x_3y_3\end{vmatrix}$ then $\Delta$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}1&a&a^2\\\sin(n-1) x&\sin nx&\sin(n+1)x\\\cos(n-1)x&\cos nx&\cos(n+1)x\end{vmatrix}$ then $\int_0^{\large\frac{\pi}{2}}f(x)dx$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are such that $\alpha+\beta+\gamma=0$ then $\begin{vmatrix}1&\cos \gamma&\cos \beta\\\cos \alpha& 1&\cos\alpha\\\cos \beta&\cos \alpha&1\end{vmatrix}$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

The value of $\begin{vmatrix}1&a&a^2-bc\\1&b& b^2-ca\\1&c&c^2-ab\end{vmatrix}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

Find the value of determinant $\begin{vmatrix}1&x&y+z\\1&y&z+x\\1&z&x+y\end{vmatrix}$

asked Nov 26, 2013 by sreemathi.v

1 answer

For all values of $A,B,C$ and $P,Q,R$ the value of the determinant

$(x+a)^3\small\begin{vmatrix}\cos(A-P)&\cos (A-Q)&\cos(A-R)\\\cos(B-P)&\cos(B-Q)&\cos(B-R)\\\cos(C-P)&\cos(C-Q)&\cos(C-R)\end{vmatrix}$ is

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are the cube roots of unity,then the value of the determinant $\begin{vmatrix}e^{\alpha}&e^{2\alpha}&e^{3\alpha}-1\\e^{\beta}&e^{2\beta}&e^{3\beta}-1\\e^{\gamma}&e^{2\gamma}&e^{3\gamma}-1\end{vmatrix}$ is equal to

asked Nov 25, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}x^n&x^{n+2}&x^{n+3}\\y^n&y^{n+2}&y^{n+3}\\z^n&z^{n+2}&z^{n+3}\end{vmatrix}$ = $(y-z)(z-x)(x-y)(\large\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$ then $n$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

If $C=2\cos \theta$ then the value of the determinant $\Delta=\begin{vmatrix}c&1&0\\1&c&1\\6&1&c\end{vmatrix}$ is

asked Nov 22, 2013 by sreemathi.v

1 answer

If one root of the determinant $\begin{vmatrix}x&3&7\\2&x&2\\7&6&x\end{vmatrix}=0$ is $-9$ then the other two roots are

asked Nov 22, 2013 by sreemathi.v

1 answer

If $a_1,a_2,a_3.....a_n$ are in G.P then the determinant $\Delta=\begin{vmatrix}\log a_n&\log a_{n+1}& \log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is equal to

asked Nov 22, 2013 by sreemathi.v

1 answer

The parameter on which the value of the determinant $\begin{vmatrix}1&x&x+1\\\cos(p-d)x&\cos px&\cos(p+d)x\\\sin(p-d)x&\sin px&\sin(P+d)x\end{vmatrix}$ does not defined upon is

asked Nov 22, 2013 by sreemathi.v

1 answer

If $a_1,a_2,a_3.......a_n$ are in G.P then the value of the determinant $\begin{vmatrix}\log a_n&\log a_{n+1}&\log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

If $D=\begin{vmatrix}1&1&1\\1&1+x&1\\1&1&1+y\end{vmatrix}$ for $x\neq 0,y\neq 0$ then $D$ is

asked Nov 21, 2013 by sreemathi.v

1 answer

If $1,\omega,\omega^2$ are the cube roots of unity ,then $\Delta=\begin{vmatrix}1&\omega^n&\omega^{2n}\\\omega^{2n}&1&\omega^n\\\omega^{2n}&1&\omega^n\end{vmatrix}$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

If $a>0$ and determinant of $ax^2+2bx+c$ is -ve then $\begin{vmatrix}a&b&ax+b\\b&c&bx+c\\ax+b&bx+c&0\end{vmatrix}$ is equal to

asked Nov 21, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}6i&-3i&1\\4&3i&-1\\20&3&i\end{vmatrix}=x+iy$ then

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $P=[a_{ij}]$ be a $3\times 3$ matrix and let $Q=[b_{ij}]$ where $b_{ij}=2^{i+j}a_{ij}$ for $1\leq i,j\leq 3$.If the determinant of P is 2,then the determinant of the matrix $Q$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

Let $\omega=-\large\frac{1}{2}$$+i\large\frac{\sqrt 3}{2}$.Then the value of the determinant $\begin{vmatrix}1&1&1\\1&-1-\omega^2&\omega^2\\1&\omega^2&\omega^4\end{vmatrix}$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

The value of the determinant $\begin{vmatrix}1 &a&a^2-bc\\1&b&b^2-ca\\1 &c&c^2-ab\end{vmatrix}$ is

asked Nov 20, 2013 by sreemathi.v

1 answer

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

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}0 &a-b&b-c\\b-a&0&b-c\\c-a&c-b&0\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate :$\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix}$

($\omega$: Cube root of unity)

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate :$\begin{vmatrix}3 &2& 12\\0 &1&8\\2&9&7\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

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