MAT223H1 Lecture 4: Lecture 4 1.5-1.8(1)
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Remark homogeneous systems arealways consistentthezero vector i is always a son to a . Homogeneous and inhomogeneous system are related bythe thmi. Thm i suppose 1 is consistent for some andp is a son the sun set of a is set of all vectors. Then oftheform where is a soi to a . Is a son ofthe corresponding homogeneous problem i 0 3 6. Yes byreducing the homogeneous matrix we obtainit 0 0 0 which corresponds to a linear system withgeneral soknetf . Some higher version ofa plane hightheorigin always a solution. In our example ii thesolus t the homogenerous problem are. Remark thetheoremuhmlolonly applies when we know the system is consistent. The systemneedstobe consistent inorder t find t f. Defin a set of vectors tpj is if mit mit only hasthe hid soin. Set (cid:1253) is called linearlydependent linearly independent in. Remark we can answerthequestion of linear dependence1 independence. Form the matrix a t the following wayi.
