If `[(1,0,0),(0,1,0),(0,0,1)][(x),(y),(z)]=[(1),(-1),(0)]` , find `x ,\ y\ a n d\ z` .

If A=[(1,0,0),(0,1,0),(0,0,1)] then A^2+2A=

|{:(x,z,0),(0,y,y),(z,0,x):}|

If A={:[(1,2,x),(0,1,0),(0,0,1)]:}, B={:[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_(3) , then find the value of x + y + 1.

Let A be a 3xx3 matric such that A . [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)] , then find A^(-1) .

The equation [1 x y][(1,3,1),(0,2,-1),(0,0,1)] [(1),(x),(y)]=[0] has i)for y=0 (p) rational roots ii) for y=-1 (q) irrational roots (r) integral roots

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,x-u=1,y-v=0,z-w=0),(,x+u=0,y+v=1,z+w=0),(,2x+3u=0,2y+3v=0,2z+3w=1):} As this system of equations is inconsistent, we say there is no right inverse for matrix A. The number of right inverses for the matrix [(1,-1,2),(2,-1,1)] is

If A=[{:(1,0,0),(1,0,1),(0,1,0):}] , then which is true (a) A^(3)-A^(2)=A-I (b) det. (A^(100)-I)=0 (c) A^(200)=[(1,0,0),(100,1,0),(100,0,1)] (d) A^(100)=[(1,1,0),(50,1,0),(50,0,1)]

The equation [[1, 2 ,2 ],[1 ,3, 4],[ 2, 4,k]][(x) ,(y), (z)] =[(0),(0), (0)] has a solution for (x ,y ,z) besides (0,0,0)dot Then the value of k is _______.

Let, I=({:(1,0,0),(0,1,0),(0,0,1):}) " and " P=({:(1,0,0),(0,-1,0),(0,0,-2):}) . Then the matrix P^(3)+2P^(2) is equal to -