Show that the functions of t: 1t, 1 + f,e'are linearly independent. Hint: if a function...
(a) Show that the functions f(t) = t2t1 and g(t) = t3 are linearly dependent on 0 < t < 1 and on -1<t< 0 (b) Show that f(t) and g(t) are linearly independent on -1 <t<1. (c) Show that W(f,g)(t) is zero for all -1<t<1.
(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t) = 5t? + 35t, g(t) = 5t2 – 35t NO_ANSWER 2. f(t) = edt cos(ut), g(t) = edt sin(ut) ,70 NO_ANSWER 3. f(x) = 51, g(x) = 5(2-3) NO_ANSWER 4. f(t) = 3t , g(t) = 1t|
(7) Show that the functions e', cos(t), ta are linearly independent in the vector space Cº. What is the dimension of the subspace of Cºo which is spanned by these three functions?
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe that they are linearly dependent (i.e. W(5,9) (+) = 0, for all t in some interval) find a dependence relation. 1. f(t) = cost, g(t) = sint 2. f(t) = 61, g(t) = 64+2 3. f(t) = 9 cos 2t, g(t) = 2 cos? t - 2 sinat 4. f(t) = 2t>, g(t) = 14
Question 5 Is the set of functions linearly dependent or linearly independent? f(x) = 7, g(x) = 5x +1, h(x) = 3x2 - 4x + 5 Linearly dependent Linearly independent Have no clue... Question 6 Given a solution to the DE below, find a second solution by using reduction of order. r’y' – 3xy + 5y = 0; y1 = r* cos(In x) y2 = xsin(In x) y2 = x2 sin Y2 = 2 * sin(In) . . y2 =...
Functions can be thought of as elements of a vector space. When we have two functions, we will make a 2x2 matrix of functions here the first row is the original functions and the second row are the first derivatives of the original functions. With three functions, we have two more rows, the first derivatives in row two and the second derivatives in row three. The matrix form is called the Wronskian. If you take the determinant and it is...
(1 point) Are the functions f, g, and h given below linearly independent? f(x) = 621 + cos(9x), g(x) = 621 – cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (e24 + cos(9x)) + (e21 – cos(9x)) + (cos(9.x)) = 0.
(1 point) Are the functions f, g, and h given below linearly independent? f(x) = €3x – cos(4x), g(x) = 23x + cos(4x), h(x) = cos(4x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (e3x – cos(4x)) + (83x + cos(4x)) + (cos(4x)) = 0.
Are the functions f(x) = x² and g(x) = xº linearly independent?
A9.4.13 Question Help Determine whether the given vector functions are linearly dependent or linearly independent on the interval (-00,00). Let x = Select the correct choice below, and fill in the answer box to complete your choice. 5t O A. The vector functions are linearly dependent since there exists at least one point tin (-00,00) where det[xy(t) x2(t)] is not 0. In fact, det[x4(t) x2(t)] - OB. The vector functions are linearly independent since there exists at least one point...