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Asked Oct 8, 2019
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{F
2а + 2b
-3a - ba,bE R? Explain why or why
2
5. Is L=
a basis for S =
4а
not
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{F 2а + 2b -3a - ba,bE R? Explain why or why 2 5. Is L= a basis for S = 4а not

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Expert Answer

Step 1

Does the set L of two vectors form a basis for the subspace S?

Step 2

To start with, S is a subspace, as it is closed under vector addition and scalar multiplication

2a+2b
S-3a-ba,be R}, is a subspace
4а
2а + 2b
as| -За -b | +| -Зс — d
2c 2d
2(a+c)+2(b+d)
-3(а+с)-b-d |E S,
4(а+ с)
4a
4c
[2a+2b
and k-3a-b
2(ka +kb)]
-3ka -kb eS
4а
4ka
help_outline

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2a+2b S-3a-ba,be R}, is a subspace 4а 2а + 2b as| -За -b | +| -Зс — d 2c 2d 2(a+c)+2(b+d) -3(а+с)-b-d |E S, 4(а+ с) 4a 4c [2a+2b and k-3a-b 2(ka +kb)] -3ka -kb eS 4а 4ka

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Step 3

Next , check that the two vectors i...

2a2b
S =-3a-ba, be R}, is a subspace
4a
1
2
-1CS.(take a 0.25, b 0.25;
Now,L-
0
a 0,b 1 for the vectors}
help_outline

Image Transcriptionclose

2a2b S =-3a-ba, be R}, is a subspace 4a 1 2 -1CS.(take a 0.25, b 0.25; Now,L- 0 a 0,b 1 for the vectors}

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