ral matixexpresseparticuleEXERCISES2.8A is TONExercises 1-4 display sets in R2. Assume the sets include thebounding lines. In each case, give a specific reason why the setH is not a subspace of R2. (For instance, find two vectors in Hwhose sura is not in H, or find a vector in H with a scalar multiplethat is not i H. Draw a picture.)7. Let viequationf A haveр3D1.а. Ноb. Hос. Is8. Let v1492.2, and 5ect linear9. With10. Within NuIn Exercissubspaceeeded t, becausee relation} is als11. А 3D3.12. А -13. Fornon4.14. FornonA.TnstancecanDetermiJustify e15.Deter-2and w =5. Let vi-53V28-5mine if w is in the subspace of R generated by vi and v2.17.

Question
Asked Nov 12, 2019
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I don't understand how to do problems 2,3,4.

ral matix
expresse
particule
EXERCISES
2.8
A is TON
Exercises 1-4 display sets in R2. Assume the sets include the
bounding lines. In each case, give a specific reason why the set
H is not a subspace of R2. (For instance, find two vectors in H
whose sura is not in H, or find a vector in H with a scalar multiple
that is not i H. Draw a picture.)
7. Let vi
equation
f A have
р3D
1.
а. Но
b. Hо
с. Is
8. Let v
14
9
2.
2, and 5
ect linear
9. With
10. With
in Nu
In Exercis
subspace
eeded t
, because
e relation
} is als
11. А 3D
3.
12. А -
13. For
non
4.
14. For
non
A.T
nstance
can
Determi
Justify e
15.
Deter-
2
and w =
5. Let vi
-5
3
V2
8
-5
mine if w is in the subspace of R generated by vi and v2.
17.
help_outline

Image Transcriptionclose

ral matix expresse particule EXERCISES 2.8 A is TON Exercises 1-4 display sets in R2. Assume the sets include the bounding lines. In each case, give a specific reason why the set H is not a subspace of R2. (For instance, find two vectors in H whose sura is not in H, or find a vector in H with a scalar multiple that is not i H. Draw a picture.) 7. Let vi equation f A have р3D 1. а. Но b. Hо с. Is 8. Let v 14 9 2. 2, and 5 ect linear 9. With 10. With in Nu In Exercis subspace eeded t , because e relation } is als 11. А 3D 3. 12. А - 13. For non 4. 14. For non A.T nstance can Determi Justify e 15. Deter- 2 and w = 5. Let vi -5 3 V2 8 -5 mine if w is in the subspace of R generated by vi and v2. 17.

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Expert Answer

Step 1

We’ll answer the first question (That is 2nd question you asked). Please submit remaining questions again one by one.

2.Consider the given diagram which represents the set H in R2

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Step 2

Assume the sets included the bounding lines.

Now, H will be a subspace of R2 if,

i).The zero vector is in H.

ii).For each u and v in H, the sum of u and v should be in H.

iii).For each u in H and scalar c, cu should be in H.

Step 3

By the given diagram it is obvious that zero vector is in H.

Now consi...

0
E H where a>0
E H and v =
0
a
0
а
which does not belong to H
Then u
0
-a
That means H is not closed under addition
Therefore, the sum of the two vectors is not on the shaded region
It implies that H is not a subspace of R2.
help_outline

Image Transcriptionclose

0 E H where a>0 E H and v = 0 a 0 а which does not belong to H Then u 0 -a That means H is not closed under addition Therefore, the sum of the two vectors is not on the shaded region It implies that H is not a subspace of R2.

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