Home
Class 12
MATHS
Find x and y if the matrix A = 1/3 [(1,2...

Find x and y if the matrix `A = 1/3 [(1,2,2),(2,1,-2), (x,2,y)]` satisfy the condition AA' =`A'A =I_3`

Text Solution

Verified by Experts

`A = 1/3[[1,2,2],[2,1,-2],[x,2,y]]`
`A' = 1/3[[1,2,x],[2,1,2],[2,-2,y]]`
Now, we are given,
`A A' = I_3`
`:. 1/3[[1,2,2],[2,1,-2],[x,2,y]]1/3[[1,2,x],[2,1,2],[2,-2,y]] = [[1,0,0],[0,1,0],[0,0,1]]`
`=>1/9[[1+4+4,2+2-4,x+4+2y],[2+2-4,4+1+4,2x+2-2y],[x+4+2y,2x+2-2y,x^2+4+y^2]] = [[1,0,0],[0,1,0],[0,0,1]]`
`=>[[1+4+4,2+2-4,x+4+2y],[2+2-4,4+1+4,2x+2-2y],[x+4+2y,2x+2-2y,x^2+4+y^2]] = 9 [[1,0,0],[0,1,0],[0,0,1]]`
`=>[[9,0,x+4+2y],[0,9,2x+2-2y],[x+4+2y,2x+2-2y,x^2+4+y^2]] = [[9,0,0],[0,9,0],[0,0,9]]`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Find x and y i the matrix A= 1/3 [[1,2,2],[2,1,-2],[x,2,y]] satisfythe condition A A\'=A\'A=I_3

Find x and y i the matrix A= 1/3 [[1,2,2],[2,1,-2],[x,2,y]] satisfythe condition A A\'=A\'A=I_3

Find the values of x,y,z if the matrix A = {:[(0,2y,z),(x,y,-z),(x,-y,z)] satisfies the equations A'A = I_3

Find the values of x,y,z if the matrix A=[(0,3y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

Find the values of x,y,z if the matrix A=[{:(0,2y,z),(x,y,-z),(x,-y,z):}] satisfy the equation A'A=I.

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .