Recent questions tagged ch4

Solve for $x$ if $\begin{vmatrix} 1 & 4 & 4 \\ 1 & -2 & 1 \\ 1 & 2x & x^2 \end{vmatrix} =0 $

asked Apr 8, 2013 by meena.p

1 answer

Show that $A=\begin{bmatrix} 1 & log_x\;y & log_x\;z \\ log_y\;x & 1 & log_y\;z \\ log_z\;x & log_z\;y & 1 \end{bmatrix}=0$

asked Apr 6, 2013 by meena.p

1 answer

Show that $A=\begin{bmatrix} xc_{r} & xc_{r+1} & xc_{r+2} \\ yc_r & yc_{r+1} & yc_{r+2} \\ zc_r & zc_{r+1} & zc_{r+2} \end{bmatrix}=\begin{bmatrix} xc_{r} & x+1c_{r+1} & x+2c_{r+2} \\ yc_r & y+1c_{r+1} & y+2c_{r+2} \\ zc_r & z+1c_{r+1} & z+2c_{r+2} \end{bmatrix}$

asked Apr 5, 2013 by meena.p

1 answer

Solve the following system of equations by matrix method:x+2y+z=7,x+3z=11,2x-3y=1.

asked Apr 5, 2013 by sreemathi.v

1 answer

Using properties of determinants, evaluate $A=\begin{vmatrix}43 & 1 & 6\\35 & 7 & 4\\17 & 3 &2\end{vmatrix}$

asked Apr 5, 2013 by sreemathi.v

1 answer

Prove that $\begin{vmatrix} (x-2)^2 & (x-1)^2 & x^2 \\ (x-1)^2 & x^2 & (x+1)^2 \\ x^2 & (x+1)^2 & (x+2)^2 \end{vmatrix}=-8$

asked Apr 5, 2013 by meena.p

1 answer

If a,b,c are positive and unequal,show that the value of the determinant $\Delta=\begin{vmatrix}a & b & c\\b & c & a\\c & a & b\end{vmatrix}$ is negative.

asked Apr 5, 2013 by sreemathi.v

1 answer

The sum of three numbers is 6.If we multiply the third number by 2 and add the first number to the result,we get 7.By adding second and third numbers to three times the first number we get 12.Use determinants to find the numbers.

asked Apr 5, 2013 by sreemathi.v

1 answer

Evaluate $\left|\begin{array}{ccc} 1 & \omega^n & \omega^{2n} \\ \omega^{2n} & 1 & \omega^{n} \\ \omega^n & \omega^{2n} & 1 \end{array}\right|$

asked Apr 4, 2013 by meena.p

1 answer

Prove that $\begin{bmatrix} x+y & x & x \\ 5x+4y & 4x & 2x \\ 10x+8y & 8x & 3x \end{bmatrix}=x^3$

asked Apr 3, 2013 by meena.p

1 answer

Without expanding evaluate the determinent $\begin{vmatrix} (a^x+a^{-x})^2 & (a^x-a^{-x})^2 & 1 \\ (a^y+a^{-y})^2 & (a^y-a^{-y})^2 & 1 \\ (a^z+a^{-z})^2 & (a^z-a^{-z})^2 & 1 \end{vmatrix}$ where $a>0$ ,and $x,y,z \in R$

asked Apr 3, 2013 by meena.p

1 answer

Evaluate : $ \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$

asked Apr 3, 2013 by meena.p

1 answer

Using the property of determinants, evalute: $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

If $\begin{vmatrix}4+x& 4-x & 4-x\\4-x & 4+x & 4-x\\4-x & 4-x & 4+x\end{vmatrix}$,then find the values of x.

asked Mar 18, 2013 by sreemathi.v

1 answer

If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]

asked Mar 15, 2013 by sreemathi.v

1 answer

If A+B+C=0,then prove that $\begin{vmatrix}1& cosC &cos B\\cos C& 1 &cos A\\cos B & cos A &1\end{vmatrix}=0.$

asked Mar 15, 2013 by sreemathi.v

1 answer

Using the properties of determinants,\[\begin{vmatrix}a^2+2a &2a+1 & 1\\2a+1 & a+2 & 1\\3 & 3 & 1\end{vmatrix}=(a-1)^3\]

asked Mar 15, 2013 by sreemathi.v

1 answer

Using matrices,solve the system of linear equations,\[2x-y+z=3\]\[-x+2y-z=-4\]\[x-y+2z=1\]

asked Mar 14, 2013 by sreemathi.v

1 answer