Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&... Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)]. Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearly dependent. Show that Vector_3 can be written as...

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Let Vector_1=[Column (1&-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&...Let Vector_1=[Column (1&-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)].Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearlydependent.
Show that Vector_3 can be written as a linear combination ofVector_1,Vector_2 and Vector_4.
Show that T={Vector_1,Vector_2,Vector_4} is linearlyindependent.
Show that the set of all linear combinations of vectors from Sis the same as the set of all linear combinations of vectors fromT.

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Let the given 4 vectors be denoted by v1v2v3v4 respectively 1 We know that dimension of R3 is 3 Therefore the set S v1v2v3v4 is linearly dependent 2 Let A be See Answer

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