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Please show work thank you! Taekıt Let ci(t) = and 22(t) = [cekit (dekat I bekat...
Please show work thank you!
Taekıt Let ci(t) = and 22(t) = [cekit (dekat I bekat (a) (6 points) Compute W[71,22](t) (b) (2 points) What conditions on a, b, c, d make ci and 22 linearly dependent? (c) (2 points) What conditions on t make wi and linearly dependent?
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) =...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y...
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y have the moment generating function My (t) i. Show that the moment generating function of Z = aY b is e*My(at) for non-zero constants a and b ii. Use the result to write down the moment generating function of W 1- 2X if X Gamma(a, B)
(a) If var[X o2 for each Xi (i...
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k...
Whats the answer to number
1?
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
Problem 5.8 Consider the motion xi = (1 t/k)X where k is a constant. From the...
Problem 5.8 Consider the motion xi = (1 t/k)X where k is a constant. From the conservation of mass and the initial condition p = po at t = 0, determine p as a function of po, t, and k
Let x(t) be the signal below: Sketch the following: (a) xi(t) = x(1 – t) (b)...
Let x(t) be the signal below: Sketch the following: (a) xi(t) = x(1 – t) (b) cz(t) = -x(t – 1) (c) 23(t) = $.- (T)dt (d) x4(t) = (t+1)x(t) () 25(t) = dr(t).
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transfor...
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transformation. (a) Prove that for every pair of ordered bases B = exists a unique m x n matrix A such that [T(E)]c = A[r3 for all e V. The matrix A is called the (B,C)-matrix of T, written A = c[T]b. (b) For each n E N, let Pm be the vector space of...
FC 1. Determine the algebra generated by {E, F). Let EFC 22. De Let N =...
FC 1. Determine the algebra generated by {E, F). Let EFC 22. De Let N = 0 – 0,1 n Q, and suppose D consists of all subsets of 12 of 0, a form (a, b) n Q. Show that AD) = P(92).
(1 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the...
(1 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the line l be x = 4t – 3, y = — (5 + 4t), z = 2 + 4t. = (20, Yo, zo) where F is parallel to l. (a) Find a point P P= Find a point Q = (x1, Yı, z1) at which F and I are perpendicular. Q - Give an equation for the set of all points at which F...
Please show work thank you!
Taekıt Let ci(t) = and 22(t) = [cekit (dekat I bekat (a) (6 points) Compute W[71,22](t) (b) (2 points) What conditions on a, b, c, d make ci and 22 linearly dependent? (c) (2 points) What conditions on t make wi and linearly dependent?
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y have the moment generating function My (t) i. Show that the moment generating function of Z = aY b is e*My(at) for non-zero constants a and b ii. Use the result to write down the moment generating function of W 1- 2X if X Gamma(a, B)
(a) If var[X o2 for each Xi (i...
Whats the answer to number
1?
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
Problem 5.8 Consider the motion xi = (1 t/k)X where k is a constant. From the conservation of mass and the initial condition p = po at t = 0, determine p as a function of po, t, and k
Let x(t) be the signal below: Sketch the following: (a) xi(t) = x(1 – t) (b) cz(t) = -x(t – 1) (c) 23(t) = $.- (T)dt (d) x4(t) = (t+1)x(t) () 25(t) = dr(t).
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> W be a linear transformation. (a) Prove that for every pair of ordered bases B = exists a unique m x n matrix A such that [T(E)]c = A[r3 for all e V. The matrix A is called the (B,C)-matrix of T, written A = c[T]b. (b) For each n E N, let Pm be the vector space of...
FC 1. Determine the algebra generated by {E, F). Let EFC 22. De Let N = 0 – 0,1 n Q, and suppose D consists of all subsets of 12 of 0, a form (a, b) n Q. Show that AD) = P(92).
(1 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the line l be x = 4t – 3, y = — (5 + 4t), z = 2 + 4t. = (20, Yo, zo) where F is parallel to l. (a) Find a point P P= Find a point Q = (x1, Yı, z1) at which F and I are perpendicular. Q - Give an equation for the set of all points at which F...
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