Evaluate matrix :

`[ [ sqrt3 , 1 , -1 ] , [ 2 , 3 , 0 ] ] + [ [ 2 , sqrt5 , 1 ] , [- 2 , 3 , 1/2] ]`

Given A=[[sqrt(3),1,-12,3,0]] and B=[[2,sqrt(5),1-2,3,(1)/(2)]], find Aquad +B

Evaluate : 1/( 1 + sqrt (2) ) + 1/( sqrt(2) + sqrt (3) ) + 1/ ( sqrt(3) + sqrt (4) )

Find ( sqrt(5) + 1 )/( sqrt(5 ) - 1) = ( A ) ( 3 + sqrt(5) )/2 ( A ) ( 3 - sqrt(5) )/2 ( A ) ( 3 + sqrt(5) )/4 ( A ) ( 3 - sqrt(5) )/4

Let alpha be a root of the equation x ^(2) + x + 1 = 0 and the matrix A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] then the matrix A ^( 31 ) is equal to :

Find the matrix A satisfying the matrix equation [(2, 1),( 3, 2)]A[(-3, 2),( 5,-3)]=[(1, 0 ),(0, 1)] .

5.Find the rank of the matrix [[2,2,-1],[4,1,2],[3,-1,0],[1,-2,-1]]

Evaluate : Find the value of sqrt( 3 + sqrt(5)) a ) sqrt(3)/2 + 1/sqrt(2) b ) sqrt(3)/2 - 1/2 c ) sqrt(5)/2 - 1/sqrt(2) d ) sqrt(5)/sqrt(2) + 1/sqrt(2)

Evaluate :   2(1/sqrt(3))^2 + 3(1/2 ) + (1/2)^2 times (sqrt3)^2

Find the matrix A satisfying the matrix equation [2 1 3 2]A[-3 2 5-3]=[1 0 0 1]

Tangents drawn from (2, 0) to the circle x^2 + y^2 = 1 touch the circle at A and B . Then (A) A-= (1/2, sqrt(3)/2) , B -= (-1/2, - sqrt(3)/2) (B) A-= (- 1/2, (-sqrt(3)/2) , B -= (1/2, sqrt(3)/2) (C) A-= (1/2, sqrt(3)/2) , B-= (1/2, - sqrt(3)/2) (D) A-= (1/2, - sqrt(3)/2), B-= (1/2, sqrt(3)/2)