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111-quiz1-sol

# 111-quiz1-sol - MATH111 Quiz 1B Solution 1[4 For each...

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MATH111 Quiz 1B Solution 1. [4] For each matrix below, determine whether its columns form a linearly independent set. Give reasons to your answers.(Avoid calculation if possible.) a. - 4 12 1 - 3 0 0 b. 1 5 - 3 2 0 4 - 9 18 0 0 0 0 (a) - 4 12 1 - 3 0 0 - 4 12 0 0 0 0 As shown above, the second column is not a pivot column. So the column vectors of the matrix are NOT linear independent. (b) 1 5 - 3 2 0 4 - 9 18 0 0 0 0 is already in echelon form. The 3 rd and 4 th column are not pivot columns. So the column vectors of the matrix are NOT linear independent. 2. [4] For each matrix in problem 1, determine if the columns of the matrix span R 3 . Give reasons to your answers.(Avoid calculation if possible.) (a) As shown in the answer of Q1, the second and the third rows are not pivot rows. So the column vectors do not span R 3 . (b) As shown in the answer of Q1, the thrid row is not a pivot row. So the column vectors do not span R 3 .

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