tps://instruct.math.lsa.umich.edu/webwork2/ma2 27-101-umd-s18/ww11 Bases for Nul

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tps://instruct.math.lsa.umich.edu/webwork2/ma2 27-101-umd-s18/ww11 Bases for Null Spaces, and Column Spaces. Rank/1 WW11 Bases for Null Spaces and Column Spaces. Rank: Problem 16 Previous Problem Problem List Next Problem (1 point) Find a basis of the subspace of IR' consisiting of all vectors of the form #1 +x2 8x1-4 51 + 8x2 Your answer should be a list of row vectors separated by commas. (Click wector to learn about entering vectors.) Basis Preview My AnswersSubmit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor Page generated at 06/182018 at 12 03am EDT WeBWork e 1996-20171 theme math4 | ww version: WeBWork-2 13 i Paversion Pa-2.13 The weeWork Project 204 AM 18/2018

Explanation / Answer

An arbitrary vector in the given subspace V(say) is of the form ( x1,2x1+x2,8x1-4x2,-5x1+8x2)T= x1(1,2,8,-5)T +x2(0,1,-4,8)T. It means an arbitrary vector in the given subspace V can be expressed as a linear combination of 2 linearly independent vectors (1,2,8,-5)T and (0,1,-4,8)T. Hence, {(1,2,8,-5)T,(0,1,-4,8)T } is a basis for the given subspace V of R4.

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