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  3. 1 given k column vectors ie r3 for i ...

Question: 1 given k column vectors ie r3 for i ...

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1. Given k column vectors ie R3 for i = 1, . . . k as follows: 0 Find all the possible groups of 3 vectors such that each group is linearly independent. Is the group (vi, V2, V. V4} 1ǐnearly independent? If it is not, please explain. 2. Given a matrix A -1 234 A=15 0-1-1 8 -6 -10 -13 (a) Show that the last row of A is a linear combination of the first two rows(i.e., we can write: the last row-αι × the first row +α-x the second row, for some αι and α, that are not simultaneously zeros (b) Let B be a 3 x 3 matrix formed by three columns of A. Is B invertible (i.e. does B-1 exist)? Does your answer depend on which three columns of A are included in B?

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