Question: With a some calculation we can get formulas to determine whether or not a set of vectors is linearly independent. (a) Show that this subset

With a some calculation we can get formulas to determine whether or not a set of vectors is linearly independent.
(a) Show that this subset of R2

is linearly independent if and only if ad - bc 6= 0.
(b) Show that this subset of R3

is linearly independent iff aei + bfg + cdh - hfa - idb - gec ‰ 0.
(c) When is this subset of R3

linearly independent?
(d) This is an opinion question: for a set of four vectors from R4, must there be a formula involving the sixteen entries that determines independence of the set? (You needn't produce such a formula, just decide if one exists.)

g/( adg

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a Assuming first that a 0 Gives which has a solution if and only if 0 cab d cb add weve assumed in this case that a 0 and so back substitution yields ... View full answer

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