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If matrix A=[[0,2y,z],[x ,y,-z],[x,-y,z]...

If matrix `A=[[0,2y,z],[x ,y,-z],[x,-y,z]]` satisfies `A'A=I`. Find the values of `x,y` and `z`

Text Solution

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Given,

`A=[[0,2y,z],[x ,y,-z],[x,-y,z]]`

`A'=[[0,x,x],[2y ,y,-y],[z,-z,z]]`

`A'A=[[0,x,x],[2y ,y,-y],[z,-z,z]][[0,2y,z],[x ,y,-z],[x,-y,z]]`

`A'A=[[2x^2,0,0],[0, 6y^2,0],[0,0,3z^2]]`

`A'A=I`

`[[2x^2,0,0],[0, 6y^2,0],[0,0,3z^2]]=[[1,0,0],[0, 1,0],[0,0,1]]`

Equating both sides

...
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