Let a_1, a_2, a_3, ...., a_p and b be vectors in R^n and A = [a_1 a_2 a_3, ...,
ID: 3036234 • Letter: L
Question
Let a_1, a_2, a_3, ...., a_p and b be vectors in R^n and A = [a_1 a_2 a_3, ..., a_p] and [Ab] = [a_1, a_2a_3, .... A_pb]. Answer each of the following questions with TRUE or FALSE. Justify your answer. b is in span{a_1, a_2, a_3, ..., a_p} (is equivalent to) the system x_1a_1 + x_2a_2 + x_2a_3 + ... x_pa_p = b is constant. b is in span {a_1, a_2, a_3, ..., a_p} rank (A) = rank [Ab] a_1, a_2, a_3, ..., a_p span R^n the system x_a_1 + x_2a_2 + x_3a_3 + .. x_pa_p = b is consistent for all b in R^n. a_1, a_2, a_3, ..., span R^n rank(A) = n If pExplanation / Answer
1) True as b is written as a linear combination of the vectvectors
2) True as then the system Ax=b will be consistent
3) True as every vector can be written as the linear combination of these vectors so they will span R^n
4) True because n linearly independent vectors are required to span R^n , and all the other vectors are linear combination of these n vectors so Rank of A is n
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