If `|[(x+1),2], [4,(x-1)]| =0` then find `x`

If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value of |[x^3-1, 0, x-x^4], [0, x-x^4, x^3-1], [x-x^4, x^3-1, 0]|

If [x\ \ 4\ \ 1][[2, 1 ,2],[ 1, 0 ,2],[ 0 ,2,-4]][[x],[4],[-1]]=0 , find xdot

If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence find a matrix X such that A^2-5A+4I+X=O .

If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

If x in [-1, 0] , then find the value of cos^(-1) (2x^(2) - 1) - 2 sin^(-1) x

If x in [-1, 0) then find the value of cos^(-1) (2x^(2) -1) -2 sin^(-1) x

If the trace of the matrix A= [{:( x-1 ,0,2,5),( 3, x^(2) - 2 ,4,1),( -1,-2,x-3,1),(2,0,4,x^(2)-6) :}] is 0 then x is equal to

If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

Find the area of the region bonded by y=x(x-1)(x-2) , the x-axis and x = 0 and x = 4.

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))