
1. Let el-el-e2 and e2-: el + e2 express the dual basis ề in terms ofe
7. [2p] (a) In a two-dimensional linear space X vectors el, e2 formi a basis. In this basis a vector r E X has expansion x = 2e1 + e2. Find expansion of the vector x in another basis 1 -2 er, e2, of X, if the change of basis matrix from the basis e to the basis e, s (b) In a two-dimensional linear space X vectors el, e2 forn a basis. In this basis a vector r E...
EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the coordinates of the vector -el+e2 with respect to the basis B. (B. {e!, e2, e) is the canonical basis) [1.5/10] Let B-lul., иг, из} and B'-fu', ua",_} be two bases of R3. where : b) 3 Calculate the change of basis matrix from B to B'
EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the...
(ii) Express the vector xo | in terms of the basis vectors | 2 | . |-1 and 0 (ii) Give an estimate for 520x
(ii) Express the vector xo | in terms of the basis vectors | 2 | . |-1 and 0 (ii) Give an estimate for 520x
1. Show the conditions for and products of an El and E2 reaction with a. cis and trans iso ne. mers of 1-chloro-2-ethylcyclohexa b. (3R,4R)-4-bromo-3-methylpent-1-ene and it's diastereomer. 2. Which stereoisomer reacts more quickly in E2 reaction - 1R,3R-1-bromo-3- methylcyclohexane, 1S,3S-1-bromo-3-methylcyclohexane, 1R,2S-1-bromo-3- romo-5-methylcyclonexane, methylcyclhexane, 1S,2R-1-bromo-3-methylchyclohexane?
12. Label the following reactions as El or E2 * 01 - 0 a . CH CH -- A. A =E1; B=E2 B.A=E1; B=E1 C. A E2: B-EI D. A=E2; B-E2 13. Consider the following exothermic E2 reaction. What rate equation would be observed for this reaction CH, CH CH I + KOC(CH3), CH CH CH2 + KI A. rate k[CHCH:CH-1) B. rate=k[CH,CH:CH:1][K OC(CH.)s] C. rate - [CH,CH:CH=1][K OC(CH);]* D. rate=k[CH,CH:CH-1)^[K OC(CH.):] E. There is not enough information given to...
Let
? be a finite-dimensional vector space,
? its dual space and
? a subspace of
.
Let
be a subspace of
and defined as follows:
Prove that
1)
2)
Question 2: Dilf Amp (el, e2, c3) 140 1 The circuit of Fig. 3 is known as an instru a. Identify the advantages of the instrumentation vi er (F on amplifier differenee amplifier (stage As). (c2) 16 pts dAfererc amph fier which is ho
A swap economy has two consumers with spending functions: el(p, u) = (3(1.5)2pįp2e4)1/3 e2(p, u) = (3(1.5)2p2p, e4)1/3 If the initial endowments are e1 = (16,0) and e2 = (0, 10), find the Walrasian equilibrium.
2. Let e1(x) = 1, ez(x) = x, p1(x) = 1 – x and p2(x) = –2 + x. Let E = (e1,e2) and B = (P1, P2). 2 a) Show that B is a basis for P1(R). 4 b) Let ce : R → R3 be the change of coordinates from E to ß. Find the matrix representation of C. Leave your answer as a single simplified matrix. 6 c) Let (:,:) be an inner product on P1(R). Suppose...
Consider the standard basis (e1, e2) of the two-dimensional Minkowski space (R1+1,m) with respect to which the metric tensor m takes the form -1 0 Consider the new basis Compute the metric matrix m with respect to the basis (L, L)
Consider the standard basis (e1, e2) of the two-dimensional Minkowski space (R1+1,m) with respect to which the metric tensor m takes the form -1 0 Consider the new basis Compute the metric matrix m with respect to the basis...