If 0<`x_1`<`x_2`<`x_3`<`pi`, then prove that `sin((x_1+x_2+x_3)/3)<(sinx_1+sinx_2+sinx_3)/3` . Hence or otherwise prove that if `A, B, C` are angles of a triangle, then the maximum value of `sinA+sinB+sinC` is `(3sqrt(3))/2`

If A=[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)] then (A) A^2=I (B) A^2=0 (C) A^3=0 (D) none of these

If A=[(a,0,0),(0,a,0),(0,0,a)],a!=0 then | adj A| is equal to

If A=[(a, 0,0),(0,b,0),(0,0,c)] and a,b,c are non zero real numbers, then A^-1 is (A) 1/(abc) [(1,0,0),(0,1,0),(0,0,1)] (B) 1/(abc) [(a,0,0),(0,b,0),(0,c,0)] (C) 1/(abc) [(a^-1,0,0),(0,b^-1,0),(0,c^-1,1)] (D) [(a^-1,0,0),(0,b^-1,0),(0,0,c^-1)]

If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)] , prove that P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P

If {:A=[(a,0,0),(0,b,0),(0,0,c)]:}," then "A^(-1) , is

If A=[(1,0,0),(0,-1,0),(0,0,2)] and B=[(2,0,0),(0, 3,0),(0,0,-1)] , find A+B , 3A+4B .

If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) [(0 ,0) ,(0, 0)] (c) [(1, 0) ,(0, 1)] (d) [(0,i) ,(i,0)]

If A=[(1,0),(2,0)] and B=[(0,0),(1,12)] then= (A) AB=0, BA=0 (B) AB=0,BA!=0 (C) AB!=0,BA=0 (D) AB!=0,BA!=0

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[[x,0, 0],[ 0,y,0],[ 0, 0,z]] , is (a) [[x^(-1),0 ,0 ],[0,y^(-1),0],[ 0, 0,z^(-1)]] (b) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

If x, y, z are non-zero real numbers, then the inverse of matrix A=[(x,0, 0) ,(0,y,0),( 0, 0,z)] is (A) [[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (B) xyz[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (C) (1)/(xyz)[[x,0,0],[0,y,0],[0,0,z]] (D) (1)/(xyz)[[1,0,0],[0,1,0],[0,0,1]]