Question

Find the values of x , y , z if the matrix satisfy the equation

Answer 1

The transpose of the matrix A is,

A'=[ 0 x x 2y y −y z −z z ]

Now,

A'A=I

[ 0 x x 2y y −y z −z z ][ 0 2y z x y −z x −y z ]=[ 1 0 0 0 1 0 0 0 1 ] [ 0+ x 2 + x 2 0+xy−xy 0−xz+xz 0+xy−xy 4 y 2 + y 2 + y 2 2zy−zy−zy 0−xz+xz 2zy−zy−zy z 2 + z 2 + z 2 ]=[ 1 0 0 0 1 0 0 0 1 ] [ 2 x 2 0 0 0 6 y 2 0 0 0 3 z 2 ]=[ 1 0 0 0 1 0 0 0 1 ]

Therefore,

2 x 2 =1 x=± 1 2

6 y 2 =1 y=± 1 6

And,

3 z 2 =1 z=± 1 3

Hence, the values are,

x=± 1 2 y=± 1 6 z=± 1 3