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Problem 3. (15 points) Let P, be the the vector space of polynomials with real coeficients and degree
less than or equal to n. Which of following is a subspace of P,,?
(0 All fanctions 了c Po that satisfy /(0) =0.
(ii) All functions 了c Pa that satisfy /(0) 二2
(ii) All fanctions 了c Pa that satisfy /(D 二0.
ce eee
Problem 4 (20 points) Let A 二 ee el where ceRande 0 Lets denote CO N0),
0 0ece
ll space and rank of the corresponding matrix, respectively.
yoyi人(.) are the column space,
(0 Find C(A), CCA7), NM(A7), ronk(A7) and dm(M(A7)).
(6 Show that C(A) 上N(A7).
Problem 5. (10 points) Let 吃 be the the vector space of polynomials with real coefficients and degree
less than or equal to 2. Determine whether or not the set of vectors (十1,z2 一3十1,2z2 十4} is line
independent.
Problem 6. (15 points) Let = RR!. Suppose
1 0
對es 同 品呈a
0 1
are subspaces of Find abasis for Ha n 102
二全三乙
三二二生
Problem 7. (15 points) Let_ Cl,外 denote aset of all the continuous functions with the domain [g,引C違
and the codomain 避 Show that G 二9 c Clg,外| 斌9(z) 站二0) sasubspace ofFCla,史
