Let a be a fixed integer. Find all integer solutions x,y,z of the system:
5x\plus{}(a\plus{}2)y\plus{}(a\plus{}2)z\equal{}a,
(2a\plus{}4)x\plus{}(a^2\plus{}3)y\plus{}(2a\plus{}2)z\equal{}3a\minus{}1,
(2a\plus{}4)x\plus{}(2a\plus{}2)y\plus{}(a^2\plus{}3)z\equal{}a\plus{}1. linear algebramatrixnumber theory unsolvednumber theory