solving equation returns 0x1 sym

I want to solve this example from a book:

This is the code:

syms r11 r12 r13 r21 r22 r23 r31 r32 r33
r11=0.766; r12=0; r13=0.643; r22=0.5;
GRB=[r11 r12 r13; r21 r22 r23; r31 r32 r33]

GRB = 

BRGGRB=GRB*GRB.';
Y=solve(BRGGRB==eye(3),[r21 r23 r31 r32 r33])

Y = struct with fields:
    r21: [0×1 sym]
    r23: [0×1 sym]
    r31: [0×1 sym]
    r32: [0×1 sym]
    r33: [0×1 sym]

But when using the solver I keep getting empty fields. I've read some other answered questions with the same problem but couldn't figure the reason for mine.

Answer 1

[Kumar Pallav]

The equation is not valid for any values of [r21 r23 r31 r32 r33]. If you change r11=1, and r13=0, you could see an output, as then the equation becomes valid.

You could see that BRGGRB(1,1) value is approximately 1 but not exactly 1. Hence, when you solve it by equating to identity matrix, it does not equate. You could try writing equations separately (refer this) and solve the equation.

[Phillip Graf]

Thank you. When I set BRGGB(1,1)=1 it works.

Is there any way to atuomate this?