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Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)...

Evaluate `|{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|`

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Evaluate |{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(z)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

|(""^(x)C_(r),""^(x)C_(r+1),""^(x)C_(r+2)),(""^(y)C_(r),""^(y)C_(r+1),""^(y)C_(r+2)),(""^(z)C_(r),""^(z)C_(r+1),""^(z)C_(r+2))|-|(""^(x)C_(r),""^(x+1)C_(r+1),""^(x+2)C_(r+2)),(""^(y)C_(r),""^(y+1)C_(r+1),""^(y+2)C_(r+2)),(""^(z)C_(r),""^(z+1)C_(r+1),""^(z+1)C_(r+2))| a)0 b) 2^(n) c) x+y+z_(C_(r)) d) x+y+""^(z)C_(r)

The determinant |^(^^)xC_(1),^(x)C_(2),^(x)C_(3)^(^^)yC_(1),^(y)C_(2),^(y)C_(3)sim zC_(1),zC_(2),zC_(3)] is equal to-

Evaluate det[[x_(C_(1)),x_(C_(2)),x_(C_(3))y_(C_(1)),y_(C_(2)),yC_(3)z_(C_(1)),z_(C_(2)),z_(C_(3))]]