. Using the wave equat check 7 whether the following function is a wave or not . where v = 2 or v2-4
(8) Suppose e, ,em) is an orthonormal list of vectors in V, and v E V. Prove that , e2 v, em)2 if and only if v Span(e.. .em) (8) Suppose e, ,em) is an orthonormal list of vectors in V, and v E V. Prove that , e2 v, em)2 if and only if v Span(e.. .em)
<C. Problem 1. For all x E R prove that r = 0 if V(e> 0) : Problem 2. For each of the below properties, name a function f: IRR that does not satisfy the property and prove your answer. (d) 3(e>0) 0) : Problem 2. For each of the below properties, name a function f: IRR that does not satisfy the property and prove your answer. (d) 3(e>0)
e:= 3. (i) Let T = (V, E) be a graph. Prove that the following are equivalent: (a) T is maximally acyclic: T does not contain a cycle but, for any u tv in V with {u, v} not in E, the graph (V, E U{e}) does contain a cycle. (b) T is minimally connected: T is connected but, for any e E E, the graph (V, E {e}) is not connected. (ii) Suppose that I (V, E) is a...
3. Prove valid by a deductive proof: 1. S (TR) 2. R R 3. (V S)-(W T)/ .. V D~W 4. Prove valid by a deductive proof: 1. (B. L)VT 2. (BVC) (~LO M) 3.~M /.. T 5. Prove valid by a deductive proof: 1. E.(FVG) 2. (E.G)(HVI) 3. (~HV I)(E . F) /.. H= I
0 2 0. Prove that a 0 or v Suppose a e F, ve V, and av 11
3. Given graph G = (V,E), prove that the following statements are equivalent. [Note: the following statements are equivalent definitions of a "tree graph".] 1) There exist exactly one path between any of two vertices u, v EV in the graph G 2) Graph G is connected and does not contain any cycles. 3) Graph G does not contain any cycles, and a cycle is formed if any edge (u, v) E E is added to G 3. Given graph...
Prove that E(x,t) = E0ei(kx-ωt) is a solution to the wave equation.
2. An electromagnetic plane wave is specified (in SI units) by E = (-68 + 3V59)et(v 3x+y)sx 10.9.42 x 1015t] Find (a) the polarization direction and amplitude of the electric field, (b) the wave propagation direction, (c) the propagation constant and the wavelength, (d) the frequency and the angular frequency, and (e) the phase velocity. 2. An electromagnetic plane wave is specified (in SI units) by E = (-68 + 3V59)et(v 3x+y)sx 10.9.42 x 1015t] Find (a) the polarization direction...
3 C. 4.5 A D. 4.5 A E. None of the above combinations is correct V 3 V 6 V 16. In the previous problem, if you take DMM #2 and flip the switch that reads "volts" to now read "amps" (ie., if DMM #2 is now also an ammeter), what happens? (Assume 20 Amp fuses) A. DMM #1 is ok., but the fuse in DMM #2 blows out-too much current! B. The fuses in both DMM #1 and DMM...