Recent questions and answers in Determinants

True or False: If the determinant $\small\begin{vmatrix}x+a & p+u & l+ f\\y+b & q+v & m +g\\z+c & r+w & n + h\end{vmatrix}$ splits into exactly $k$ determinants of order $3$, each element of which contains online term,then the value of $k$ is $8$.

answered Dec 6, 2017 by priyanka.c

1 answer

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

answered Dec 21, 2016 by priyanka.c

1 answer

Without expanding show that $\begin{vmatrix} x^2+x & x+1 & x-2 \\ 2x^2 +3x-1 & 3x & 3x-3 \\ x^2+2x+3 & 2x-1 & 2x-1 \end{vmatrix} = xA +B$ Also find A and B.

answered Dec 9, 2016 by priyanka.c

1 answer

Using cofactors of elements of second row, evaluate $\triangle = \begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}$

answered Dec 5, 2016 by priyanka.c

1 answer

$ \text{If } \Delta = \begin{vmatrix} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \\ a_{31}&a_{32}&a_{33} \end{vmatrix} \text{ and } A_y \text{ is Cofactor of } a_y \text{, then the value of } a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}=? $

answered Feb 11, 2014 by rvidyagovindarajan_1

1 answer

$ \text{If } \begin{vmatrix} 2 x&5 \\ 8&x \end{vmatrix} = \begin{vmatrix} 4&5 \\ 8&3 \end{vmatrix},then\; x\; is\; equal\; to$

answered Jan 31, 2014 by rvidyagovindarajan_1

1 answer

If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $\;\large\frac{-1}{xyz}$ is

answered Jan 30, 2014 by balaji.thirumalai

1 answer

If $A= \; \begin{bmatrix} 1& 0 &0 \\ 2 & 3 & 4\\ 0&1 & 2 \end{bmatrix}$, then the value of $A.(Adj\:A)$ is?

answered Jan 30, 2014 by rvidyagovindarajan_1

1 answer

Evaluate: $ \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}$

answered Dec 22, 2013 by balaji.thirumalai

1 answer

If the following matrix is singular, what is the value of $x: \; \begin{bmatrix} -3& -5 &1 \\ 9 & 14 & 1\\ 7+x&29 & -2 \end{bmatrix}$

answered Dec 22, 2013 by balaji.thirumalai

1 answer

determinants

asked Oct 25, 2013 by sharon.r.varghese_1

0 answers

Using matrices, solve the following system of equations:$x+\frac{2}{y}+3xz=-1,2x-\frac{4}{y}-3xz=3,3x+\frac{6}{y}-2xz=4$

answered Apr 9, 2013 by meena.p

1 answer

Find the area of the triangle where vertices are $A(11,7),B(5,5)\; and\; C(-1,3)$

answered Apr 8, 2013 by meena.p

1 answer

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

answered Apr 8, 2013 by meena.p

1 answer

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

answered Apr 6, 2013 by meena.p

1 answer

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

answered 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.

answered Apr 5, 2013 by sreemathi.v

1 answer

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

answered Apr 5, 2013 by sreemathi.v

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.

answered 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.

answered Apr 5, 2013 by sreemathi.v

1 answer

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

answered Apr 4, 2013 by meena.p

1 answer