Let this cluster to be a subspace of V. Find an orthonormal base
for W.
V = R3 ve W =< (1,0, -1),(0,1, -1) >
5. ??? v. (0) = 20Y ?? v, v * ??? i ?????? t> 0
5. Let v(0) 20V. Find vov and i, for t>o 8? 5? 20.5FC Figure.5
4. [25 pts] Consider the following circuit: 2V + 222 112 V V w 10 V + 32 12 422 > a. [15 pts] Find V, and V, using mesh analysis. b. [10 pts) What is the current through the 42 resistor.
1. Find v(t) fort> 0 in the circuit in below: t=0 222 w 622 w + 10V 2 F +1 50 V Assume the switch has been open for a long time and is closed at t=0.
a. Let W and X both be subspaces of a vector space V. Prove that dim(WnX) > dim(W) + dim(X) - dim(V) b. Define a plane in R" (as a vector space) to be any subspace of dimension 2, and a line to be any subspace of dimension 1. Show that the intersection of any two planes in R' contains a line. c. Must the intersection of two planes in R* contain a line?
Given the following vectors: ū= 3 ū= W = > (a) Find the projection of ū onto ū. BOX YOUR ANSWER. (b) Find the projection matrix of the projection in part (a). BOX YOUR ANSWER. (c) Find the projection of ū onto the subspace V of R3 spanned by ✓ and W. (You may use MATLAB for matrix multiplication in this part, but you must provide the expressions in terms of matrices.) BOX YOUR ANSWER. (d) Find the distance from...
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
(b) If R = 4solve and sketch the response of voltage, V(t) when t > 0. Next, obtain the current I flowing through the inductor in Figure Q3(b). [16 marks) t = 0 422 IH wm + + 24 V 0.25 F V(t) R Figure Q3(b)
2. In each of the following find out if the subset S is a subspace of the vector space V. (a) V = R3, S = {x = (x1,T2, xs) : 2x1-3x2 +23 = 6). 一 山 (c) V = R2, S = {x = (xi, X2) : X1X2 > 0}
Question 4 Find i(t) for t >0 for the circuit below. 4Ω 12 V 5 H 3 A