Determine if the following sets are bases for the indicated vector space. Hint: If you know the dimension of the vector space, then you only need to check that either S is linearly independent or S is a spanning set (not both), as long as S has the correct number of vectors. (a) S = {1 + 2x + x², 1+x²,1+x} C P₂. (b) S {1+x² + x³, x −– x² x², x³. 1} CP3. [1] [4]} = (c) S = {[ 3 2 0 " CM2,2. + Drag and drop an image or PDF file or click to browse... Consider the subspace W = {(a, 2b, a - -36,0) a,b ≤ R} of R4. : (a) Find a basis for W. Show your work. (b) What is dim(W)?

Determine if the following sets are bases for the indicated vector space. Hint: If you know the dimension of the vector space, then you only need to check that either S is linearly independent or S is a spanning set (not both), as long as S has the correct number of vectors. (a) S = {1 + 2x + x², 1+x²,1+x} C P₂. (b) S {1+x² + x³, x −– x² x², x³. 1} CP3. [1] [4]} = (c) S = {[ 3 2 0 " CM2,2. + Drag and drop an image or PDF file or click to browse... Consider the subspace W = {(a, 2b, a - -36,0) a,b ≤ R} of R4. : (a) Find a basis for W. Show your work. (b) What is dim(W)?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 33EQ

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