Decompose v into two vectors V, and V2, where V, is parallel to w and v2 is orthogonal to w. v=i-5j, w = 3i+j 1 29 3 7 O A. Vy=-51+ - 51, V2 = -51 5) 3 1 6 24 O B. Vy = - 51+ - 51, V2 = 51 5 3 1 8 24 OC. V = 5+ - 51, V2 = 51+ 2 2 5 43 OD. Vq = - 31+ - g), V2 = 3i+-gi
3 1 Lety 1 1 V and V2 Find the distance from y to the subspace W of R* spanned by V, and V. given that the closest point to y in W - 2 -1 2 0 13 الميا - 1 -5 is y 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed)
(1) Prove that QV2+3) Q(V2, V3) (2) Prove that (Q(V2, v3):Q) 4 (3) Find the minimal polynomial of V2 + V/3 overQ.
Q 3) Find v1, V2 and v3. + 30 V – + 20 V – - 50 V + + v2- 40 V
Find the node voltages v1, v, and v2. Use nodal analysis. R3 R 2 17 3 1 2 Given Variables: R1:2 ohm R2 1 ohm R3 1 ohm R4 2 ohm Vs:5 V Is : 1 A
show units! ] Find V., V2 ] Find Ave A 39 31 SVB 3] Find Vw, I,
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Ci-00 o Vo Qi RL-10k2 6 5 V Figure 2. I-500 μΑ, ka'(W/L)-1 mA/V2, IVI î.5V, VA-75V For the circuit shown in Figure 2: a) Find VD, Va, and Vas b) Draw a small signal equivalent circuit and find the model parameter values. c) Find the input and output resistances of the circuit. d) Find the open circuit voltage gain for the amplifier and the loaded voltage gain.
NAME: 6) Find V1 and V2 for the circuit below. (30 Points) t: J2a2 V 2 -JS2 -)232 SIS2
Decompose v into two vectors, V, and v2, where v, is parallel to w and v2 is orthogonal to w. V= -1 + 2), w=i+2) V1 = i + V2 = ((i+O; (Simplify your answer.)