Consider the following set of vectors S= (V1, V2, V3, V4) in the vector space of...

  

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Consider the following set of vectors S= (V1, V2, V3, V4) in the vector space of 2x2 matrices: VI ((4.-1)|(2.2)): V2 = ((-2,5) (4, 12)); V3 V4 ((1.2)|(3, 7)): ((-3.3)|(1,5)): [43] (4.1) (0) Study linear dependence of vectors in this set to show that the set is linearly dependent, and identify a subset U of linearly independent vectors in S Express the vectors of S which are not included in U in the form of linera combination of vectors in U. (b) Is it possible to express the vector V2 in the form of linear combination of vectors V1, V3 and V4? Write such linear combination or argue why that is impossible. Consider the following set of vectors S= (V1, V2, V3, V4) in the vector space of 2x2 matrices: VI ((4.-1)|(2.2)): V2 = ((-2,5) (4, 12)); V3 V4 ((1.2)|(3, 7)): ((-3.3)|(1,5)): [43] (4.1) (0) Study linear dependence of vectors in this set to show that the set is linearly dependent, and identify a subset U of linearly independent vectors in S Express the vectors of S which are not included in U in the form of linera combination of vectors in U. (b) Is it possible to express the vector V2 in the form of linear combination of vectors V1, V3 and V4? Write such linear combination or argue why that is impossible.