The value of the determinant `|[x,x-1],[x-1,x]|` is

The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is equal to

The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is equal to

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

The value of the determinants |{:(1,a,a^(2)),(cos(n-1)x,cos nx , cos(n+1)x),(sin(n-1)x , sin nx , sin(n+1)x):}| is zero if

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)

The value of the determinant of n^(t h) order, being given by |[x, 1, 1...], [1, x, 1...], [1, 1, x...],[... , ... , ...]| is a. (x-1)^(n-1)(x+n-1) b. (x-1)^n(x+n-1) c. (1-x)^(-1)(x+n-1) d. none of these

If the maximum and minimum values of the determinant |(1 + sin^(2)x,cos^(2) x,sin 2x),(sin^(2) x,1 + cos^(2) x,sin 2x),(sin^(2) x,cos^(2) x,1 + sin 2x)| are alpha and beta , then

Find the value of x if i) |[x^(2)-x+1,x+1],[x+1,x+1]|=0

Without expanding, show that the value of each of the determinants is zero: |[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|

By using properties of determinants. Show that: |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2