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1-4 Key Question #15 (Total: 25 marks) 1. The diagram below shows two squares. Express each difference as a single...
ne diagram below shows two squares. Express each difference as a single vector Show all intermediate steps (i.e. equivalent vectors that you need to use to solve for the difference) (6 marks: 1/1/2/2) d. AE ED a. DB-DE b. BE-BA c. AC-BD F E A 2. Copy each set of vectors and draw u-v. (4 marks: 1/2/1) a. b. C. No t 3 ne diagram below shows two squares. Express each difference as a single vector Show all intermediate steps...
Can u please answer the question (G) 1. (15 marks total) Consider the real vector space (IR3, +,-) and let W be the subset of R3 consisting of all elements (z, y, z) of R3 for which z t y-z = 0. (Although you do not need to show this, W is a vector subspace of R3, and therefore is itsclf a rcal vector space.) Consider the following vectors in W V2 (0,2,2) V (0,0,0) (a) (2 marks) Determine whether...
How does one solve this problem? 4. (a) Consider the vector space consisting of vectors where the components are complex numbers. If u = (u1, u2, u3) and v = (V1,V2, us) are two vectors in C3, show that where vi denotes the complex conjugate of vi, defines a Hermitian (compler) inner product on C3, i.e. 1· 2· 3, 4, (u, v) = (v, u), (u+ v, w)=(u, w)+(v, w), (cu, v) = c(u, v), where c E C is...
Question 4 (15 marks) Figure 4 shows a single-phase diode bridge rectifier supplied from the 230 V, 50 Hz mains via a step- down transformer D2 D SW + n: 1 + 230 V 33mF 20 0 Vo 50 Hz D3 D4 Figure 4 (a) Assuming that the switch SW is open, explain the operation of the rectifier in figure 4 with the aid of the waveforms of the input and output voltages (v, and v) [4 marks (b) With...
please give some explanation to each step 15 Total Question 3 Let F: R3R3 be any C2 vector field. 3(a). Prove that the divergence of the curl of F is zero. /4 marks 3(b). For F as defined above, a misguided professor claims that for any closed curve C, F dr 0 because of the argument: (x F)ds F-dr div (eurl F) dV X 0-APO by using Stokes' theorem, the divergence theorem, and then part (a) for an appropriately chosen...
1 Question 3 (4 Marks) show key steps Consider the vector space M2x2(C). i Let Z Span 2 + 3i 2 - 31 2i -2i Is Z? -1+i 10+ 1li s(-
2. (-/1 Points] DETAILS POOLELINALG4 6.1.003. MY NOTES Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space. If it is not, select all of the axioms that fail to hold. (Let u, v, and w be vectors in the vector space V, and let c and d be scalars.) The set of all vectors [] in R2 with xy > 0 (i.e., the union of the first and third quadrants),...
Question 1 (2+2+5 marks] (a) Find the angle between the vectors y =(4,0,3), v = (0,2,0). (b) Consider the subspace V (a plane) spanned by the vectors y, V. Find an orthonormal basis for the plane. (Hint: you may not need to use the full Gram-Schmidt process.) (c) Find the projection of the vector w=(1,2,3) onto the subspace Vin (b). Hence find w as a sum of two vectors wi+w, where w, is in V and w, is perpendicular to...
Question 3. 25 marks This question is about the downlink of a two user system, with one base station (BS) sending signals to two users, denoted user 1 and user 2. The BS is equipped with an array of n antenna elements, and each user has a single antenna. The system is a flat fading scenario, with a single complex channel coefficient from each BS antenna to each user in the base-band channel representation. We denote the channel coefficients from...
answer this . will rate after Given the vectors u = (1, -2,1), v= {5,–4,0) and w = (3,0,-2) (6 points) a) Graph u, v, and was position vectors and label each vector. Show your calculation or justify your reasoning (4 points) b) To the nearest degree, what is the angle between the vectors u and w. (6 points) c) Write the equation of the plane containing the vectors u and w (4 points) d) Determine if the vectors u,...