that is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies that E-U
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That is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies th...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) =...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Problem 5. Let W and U be finite-dimensional vector spaces, and let T : W > W and S : W -> U be linear transforma...
Problem 5. Let W and U be finite-dimensional vector spaces, and let T : W > W and S : W -> U be linear transformations. Prove that if rank(S o T) L W W such that S o T = So L. = rank(S), then there exists an isomorphism (,.. . , Vk) is a basis of ker(T), and let (w1, ., wr) is a basis of im(T) nker(S) if 1 ik Hint: Let B (vi,... , Vk,...,vj,) be...
e s t 20 Based on that w Mint Denver dot show up for the fir...
e s t 20 Based on that w Mint Denver dot show up for the fir Reservation for an are with 255 (a) What is the probability that personlig L mber of people the w represent there who wowo t u e to the dat i Use them question what is the h o ng e a) What is the e Let A bete evento per persones for PA) AM) vinc th nt theme that e how PA) Let w...
6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution...
6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution of the Cauchy problem for the heat equation u = kuyx - < x <®, t> 0, (5.17) with initial condition u(t,0) = {(H(x + 1) - H (1 - x)) in terms of the error function Erf () = * e ** dy.
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)...
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)nuln] + (-))' hnnDetermine vinl -h) rin) for -00n< oo using graphical convolution(s)
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00
Problem 6. Let V, W, and U be finite-dimensional vector spaces, and let T : V → W and S : W → U be linear transformatio...
Problem 6. Let V, W, and U be finite-dimensional vector spaces, and let T : V → W and S : W → U be linear transformations (a) Prove that if B-(Un . . . , v. . . . ,6) is a basis of V such that Bo-(Un .. . ,%) s a basis of ker(T) then (T(Fk+), , T(n)) is a basis of im(T) (b) Prove that if (w!, . . . ,u-, υ, . . . ,i)...
Given h(t)=(e-t+e-3t)u(t) find: A) The transfer function H(s). B) The locations of all poles and zeros....
Given h(t)=(e-t+e-3t)u(t) find: A) The transfer function H(s). B) The locations of all poles and zeros. C) Determine if the system is stable or not D) Find the differential equation for this system.
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1), ...,T(un)} is linearly dependent, then the set {V1, ..., Un} is linearly dependent as well. Hint: use part (a).
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) =...
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Problem 5. Let W and U be finite-dimensional vector spaces, and let T : W > W and S : W -> U be linear transformations. Prove that if rank(S o T) L W W such that S o T = So L. = rank(S), then there exists an isomorphism (,.. . , Vk) is a basis of ker(T), and let (w1, ., wr) is a basis of im(T) nker(S) if 1 ik Hint: Let B (vi,... , Vk,...,vj,) be...
e s t 20 Based on that w Mint Denver dot show up for the fir Reservation for an are with 255 (a) What is the probability that personlig L mber of people the w represent there who wowo t u e to the dat i Use them question what is the h o ng e a) What is the e Let A bete evento per persones for PA) AM) vinc th nt theme that e how PA) Let w...
6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution of the Cauchy problem for the heat equation u = kuyx - < x <®, t> 0, (5.17) with initial condition u(t,0) = {(H(x + 1) - H (1 - x)) in terms of the error function Erf () = * e ** dy.
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)nuln] + (-))' hnnDetermine vinl -h) rin) for -00n< oo using graphical convolution(s)
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00
Problem 6. Let V, W, and U be finite-dimensional vector spaces, and let T : V → W and S : W → U be linear transformations (a) Prove that if B-(Un . . . , v. . . . ,6) is a basis of V such that Bo-(Un .. . ,%) s a basis of ker(T) then (T(Fk+), , T(n)) is a basis of im(T) (b) Prove that if (w!, . . . ,u-, υ, . . . ,i)...
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1), ...,T(un)} is linearly dependent, then the set {V1, ..., Un} is linearly dependent as well. Hint: use part (a).
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).
Q4. Let T :V + W be a one-to-one linear transformation (i.e. an equation T(u) = T(v) always implies u = v). (a) Show that the kernel of T contains only the zero vector. (b) Show that if the set {T(v1),...,T(Un)} is linearly dependent, then the set {01, ..., Un} is linearly dependent as well. Hint: use part (a).
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