Matrix `[{:(1,0),(0,1):}]`is :

Let A denote the matrix ({:(0,i),(i,0):}) , where i^(2) = -1 , and let I denote the identity matrix ({:(1,0),(0,1):}) . Then I + A + A^(2) + "….." + A^(2010) is -

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y_(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of reflection about the line y=x .

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of reflection about the line y=x .

The identity matrix I_(2)={:[(1,0),(0,1)]:} . If A={:[(2,-3),(5,1)]:} , evaluate AI_(2)=I_(2)A=A

Find the rank of the matrix A = [(1,0),(0,1)]

If A=[(costheta, sin theta),(-sintheta, costheta)] then lim_(nrarroo) A^n/n is (where theta epsilon R) (A) an idenity matrix (B) a zero matrix (C) [(1,0),(0,1)] (D) [(0,1),(-1,-0)]

The matrix A=({:(0,1),(-1,0):}) is ……

Find the rank of the matrix A = [(1,1),(0,0)]

Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]