Math 54, Summer 2009, Lecture 4Worksheet 1: Lay 1.7(1) Classify the following sets as linearly indep endent or linearly dependent. (Hint: manydon’t require calculation).(a)123,000,456.(b)232,105,1−32.(c)12,34,56.(d)1−10,01−1,−101.(e)1−23−4,−3−69−12.1(2) True or False: The columns of a matrix A are linearly dependent if and only if theequation A~x =~0 is consistent. Justify your answer.(3) Suppose ~v1, . . . , ~v4are vectors in R3. Let S2= {~v1, ~v2}, S3= {~v1, ~v2, ~v3}, and S4={~v1, ~v2, ~v3, ~v4}. For each of the following, mark the statement true or false. As always,justify your answer.(a) If Span S4= R3, then Span S3= R3.(b) If Span S3= R3, then Span S4= R3.(c) If S2is linearly dependent, then so is S3.(d) If S3is linearly dependent, then so is
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