s 1-4 display sets in R2. Assume the sets include the n lines. In each case, giv

Question

s 1-4 display sets in R2. Assume the sets include the n lines. In each case, give a specific reason why the set bouo a subspace of R. (For instance, find two vectors in H H is is not in H, or find a vector in H with a scalar multiple nding 7. Let v-1- that is not in H. Draw a picture.) p=1-10 a. How man b. How man c. Is p in Co 8. Let v1 14 . Det 2. 9. With A and 10. With u=( in Nul A. In Exercises 11 a subspace of RPa to se on 50 11. A=1-9 12, A=1-5 13. For A as in nonzero ve 14. For A as in nonzero ve Determine whi Justify each ans

Explanation / Answer

1) The set H is the first quadrant of plane. It is not a subspace of R^2 because it is not closed under scalar multiplication.

Note that the point (1,1) lies in H but if we multiply it by -1, we get -1*(1,1)=(-1,-1) which is not a part of H.

2) Not that u=(2,1) lies in first quadrant, and v=(-1, -2) lies in third quadrant. If we add them up we get (1, -1) which lies in fourth quadrant, hence it is not a subspace.

3) Not that (-a, 0) lies in the set for a very small. However, for large number b, b(-a, 0) does not lies in that set. Hence it is not a subspace.

4) Note that (1,1) lies in the set but -1(1,1)=(-1,-1) does not lie in the given set and hence it is not a subspace.

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