m20f_mdtm_twosol

# m20f_mdtm_twosol - is invertible or not If so ﬁnd the...

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Unformatted text preview: is invertible or not. If so, ﬁnd the inverse; if no, give reasons. Show all the computational steps of how you get the answer. 2. (20 points) Find the dimension and a basis for the subspace span{v1, v2, v3, v4, v5} Where 2 ,vs— _6- 9 COMP-‘0 l —3 1 171 z 0 7 U2 : 7 U3 : —4 a U4 3 —3 —3 l —8 2 — 6 7 Show all the computational steps of how you get the answer. f ;. ’ I V V _ I \/1 2, 7> V4 V c 3. (15 points) Let A 2 [a1 a2 a3 a4 a5] E RSXE’ and B = [a2 a3 a4 a5 (11]. If det(A) = 49, what is det(B)? Show all the computational steps of how you get the an— swer. MCQVQE ac? a: at] 3r 2(4) 0(6F [617’ a; a? al 43'] 3f : a 3 61‘ a4 (ls—3 4. (15 points) Let 73 be the space of all univariate polynomials and deﬁne H as H: {1303) e 7: : [113mm : 1 +p(0)}. Determine Whether H is a subspace of 73 or not. Explain your reasons. 974mg” Na; 27 § H 176% gojtaﬁmo [0 Nil) H a m 0W Ma Mm M g piél’l/ We F1 ¥H {RR (7f L‘éem 1650067? :- Sipwﬁ+gce)& =Z+ PfaHﬂo) \ __ :k H Mania; pep/v01 dwl mgw WW )4 Lﬂéfl bmdalﬂﬂmaﬂﬁ W ' Sawyer: ozg'poapﬁf; O(+0(*PZ‘) 2}: Help/a) #01:}; H/DA/Dl/Aéilrafﬂqu’l’l g/ f \ a 5. (15 points) Let A E Rmxm and B E Rmxn be two matrices. Suppose A is invertible. Prove that if a: E Nul(AB), then x E Nul(B). Weak/“1643):? 491% Bl 6. (15 points) Let A E Rn” be a square matrix. Prove that if A2 is invertible, then A is also invertible. 'L 4M; A A» WHLQ/ Mgﬂko g, 1 Mai m 164(42): W)~W§:dd[A—) g; ...
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m20f_mdtm_twosol - is invertible or not If so ﬁnd the...

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