Homework Answers
Let this cluster to be a subspace of V. Find an orthonormal base for W. V...
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....
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...
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 +...
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)...
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?
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
Given the following vectors: ū= 3 ū= W = > (a) Find the projection of ū...
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...
(b) If R = 4solve and sketch the response of voltage, V(t) when t > 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...
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...
Question 4 Find i(t) for t >0 for the circuit below. 4Ω 12 V 5 H 3 A
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?
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
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...
(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
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