# solving equation returns 0x1 sym

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Phillip Graf on 30 Aug 2021
Commented: Phillip Graf on 7 Sep 2021
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.

Kumar Pallav on 2 Sep 2021
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.
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Phillip Graf on 7 Sep 2021
Thank you. When I set BRGGB(1,1)=1 it works.
Is there any way to atuomate this?

R2020a

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