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# HW4 - Math 3013 Homework Set 4 Problems from 1.6(pgs 99-101...

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Math 3013 Homework Set 4 Problems from § 1.6 (pgs. 99-101 of text): 1,3,5,7,9,11,17,19,21,24,26,35,37,38 1. (Problems 1.6.1, 1.6.3, 1.6.4, 1.6.7, 1.6.9 in text). Determine whether the indicated subset is a subspace of the given R n . (a) W = { [ r, - r ] | r R } in R 2 (b) W = { [ n,m ] | n and n are integers } in R 2 (c) W = { [ x,y,z ] | x,y,z R and z = 3 x + 2 } in R 3 (d) W = { [ x,y,z ] | x,y,z R and z = 1, y = 2 x } in R 3 (e) W = { [2 x 1 , 3 x 2 , 4 x 3 , 5 x 4 ] | x i R } in R 4 2. (Problem 1.6.11 in text). Prove that the line y = mx is a subspace of R 2 . (Hint: write the line as W = { [ x,mx ] | x R } .) 3. (Problems 1.6.17, 1.6.19 and 1.6.21 in text). Find a basis for the solution set of the following homogeneous linear systems. (a) 3 x 1 + x 2 + x 3 = 0 6 x 1 + 2 x 2 + 2 x 3 = 0 - 9 x 1 - 3 x 2 - 3 x 3 = 0 (b) 2 x 1 + x 2 + x 3 + x 4 = 0 x 1 - 6 x 2 + x 3 = 0 3 x 1 - 5 x 2 + 2 x 3 + x 4 = 0 5 x 1 - 4 x 2 + 3 x 3 + 2 x 4 = 0 (c) x 1 - x 2 + 6 x 3 + x 4 - x 5 = 0 3 x 1 + 2 x 2 - 3

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HW4 - Math 3013 Homework Set 4 Problems from 1.6(pgs 99-101...

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