# MRQ2 - UCSC AMS 10 FALL 2009 Review For Midterm 2(1...

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UCSC AMS 10 FALL 2009 Review For Midterm 2 (1) Consider the set of vectors B = 1 1 1 , 2 0 - 1 , 0 1 1 . a. Show that B is a basis of R 3 . b. Find 2 4 1 2 3 3 5 B , (the coordinate vector of 2 4 1 2 3 3 5 with respect to the basis B ). c. Find the change of basis matrix from the basis B to the basis C = 1 1 1 , 1 1 0 , 1 0 0 . (2) Given below are a matrix A and its reduced row echelon form. Find rank( A ) and bases for the column space of A , the row space of A and the null space of A . A = 1 2 0 - 2 7 2 3 1 0 5 2 - 1 5 4 - 7 0 - 2 2 2 - 6 1 0 2 0 1 0 1 - 1 0 1 0 0 0 1 - 2 0 0 0 0 0 (3) Consider the three vectors below. v 1 = 1 2 1 3 , v 2 = - 1 0 2 5 , and v 3 = 3 4 0 1 . a. What is the dimension of the subspace V = span( v 1 , v 2 , v 3 )?

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