Please do parts a, b, c
One application of linear transformations is to solving differential equations. Given a polynomial f ∈ P2, we want to consider polynomials y ∈ P2 satisfying the differential equation.
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I am confused about how to solve (b) (c) (d) (4) (Interpolating polynomials) Say we want...
I am confused about how to solve (b) (c) (d)
(4) (Interpolating polynomials) Say we want to find a polynomial f(x) of degree 3, satisfying some interpolation conditions. In each case below, write a system of linear equations whose solutions are (ao, a1, a2, az). You don't need to solve. (a) We want f(x) to pass through the points(1,-1), (1, 2), (2,1) and (3,5). (b) We want f(x) to pass through (1,0) with derivative +2 and (2,3) with derivative-1 (c)...
Help A3: This question illustrates how different bases for spaces of polynomials can help solv- ing...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
Do just the marked ones (21,22,25) PART III. Given these pairs of differential operators, what operator...
Do just the marked ones (21,22,25)
PART III. Given these pairs of differential operators, what operator is the com- sition of the operators? Multiply the two characteristic polynomials and construct the composite operator by inspection. L20) y" y 23. L1()" - 5y 24. Li (y) = y" + y; L2() +2y L2(y) = y" + y PART IV. Nonhomogeneous differential equations with constant coefficients. For the following differential equations, factor the characteristic polynomials of the op- erator and of an...
Differential equations. Please answer all parts of the question! 1.Consider the linear second-order ODE +2y 0....
Differential equations. Please answer all parts of the question!
1.Consider the linear second-order ODE +2y 0. (A) What is the "characteristic polynomial"? (B) What is the "characteristic equation"? And what are the roots? (C) What is the general solution to the ODE? 2.Find the general solution to 324u-y
A polynomial p(x) is an expression in variable x which is in the form axn + bxn-1 + …. + jx + k, where a, b, …, j, k are...
A polynomial p(x) is an expression in variable x which is in the form axn + bxn-1 + …. + jx + k, where a, b, …, j, k are real numbers, and n is a non-negative integer. n is called the degree of polynomial. Every term in a polynomial consists of a coefficient and an exponent. For example, for the first term axn, a is the coefficient and n is the exponent. This assignment is about representing and computing...
solve them by step , thank yooooooou 1. Consider the matrix A = [ 24 31....
solve them by step , thank yooooooou
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change...
Please solve it clear . In clear hand write . Thankyoooou 1. Consider the matrix A...
Please solve it clear . In clear hand write . Thankyoooou
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain...
HW08 vector spaces subspaces: Problem 8 Next Problem Previous Problem Problem List (1 point) Determine whether...
HW08 vector spaces subspaces: Problem 8 Next Problem Previous Problem Problem List (1 point) Determine whether the given set S is a subspace of the vector space V. f those functions satisfying f(a) = f(b). A. V is the vector space of all real-valued functions defined on the interval la, b, and S is the subset of V consisting B. V C1 (R), and S is the subset of V consisting of those functions satisfying f'(0) > 0. , _D...
Please solve them clear . 1. Consider the matrix A = [ 24 31. a) (7...
Please solve them clear .
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above...
I quite weak at vector spaces. Can anyone tell me n the reason behind it? 13:02...
I quite weak at vector spaces. Can anyone tell me n
the reason behind it?
13:02 Previous Problem List Next (1 point) Determine whether the given set S is a subspace of the vector space V A, V = C2(1), and s is the subset of V consisting of those functions satisfying the differential equation y4y' 3y0 B. V2, and S is the set of all vectors (z1,2) in V satisfying 516r2 0 C. V, and S is the subset...
I am confused about how to solve (b) (c) (d)
(4) (Interpolating polynomials) Say we want to find a polynomial f(x) of degree 3, satisfying some interpolation conditions. In each case below, write a system of linear equations whose solutions are (ao, a1, a2, az). You don't need to solve. (a) We want f(x) to pass through the points(1,-1), (1, 2), (2,1) and (3,5). (b) We want f(x) to pass through (1,0) with derivative +2 and (2,3) with derivative-1 (c)...
Help
A3: This question illustrates how different bases for spaces of polynomials can help solv- ing mathematical problems. In particular, we look at the use of Lagrange polynomials for polynomial interpolation. Let be the space of polynomials of degree at most two. (a) We define the mapping T: P2R3 by evaluating a given polynomial f i.e P2 at 12,, T(f) = f(2) f(3) Show that this is a linear transformation. (b) Consider the bases B b, b2, bs1,t, and G9929s),...
Do just the marked ones (21,22,25)
PART III. Given these pairs of differential operators, what operator is the com- sition of the operators? Multiply the two characteristic polynomials and construct the composite operator by inspection. L20) y" y 23. L1()" - 5y 24. Li (y) = y" + y; L2() +2y L2(y) = y" + y PART IV. Nonhomogeneous differential equations with constant coefficients. For the following differential equations, factor the characteristic polynomials of the op- erator and of an...
Differential equations. Please answer all parts of the question!
1.Consider the linear second-order ODE +2y 0. (A) What is the "characteristic polynomial"? (B) What is the "characteristic equation"? And what are the roots? (C) What is the general solution to the ODE? 2.Find the general solution to 324u-y
solve them by step , thank yooooooou
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change...
Please solve it clear . In clear hand write . Thankyoooou
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain...
HW08 vector spaces subspaces: Problem 8 Next Problem Previous Problem Problem List (1 point) Determine whether the given set S is a subspace of the vector space V. f those functions satisfying f(a) = f(b). A. V is the vector space of all real-valued functions defined on the interval la, b, and S is the subset of V consisting B. V C1 (R), and S is the subset of V consisting of those functions satisfying f'(0) > 0. , _D...
Please solve them clear .
1. Consider the matrix A = [ 24 31. a) (7 pnts) Find the characteristic polynomial of A. b) (7 pnts) Compute the matrix B = A- 2A +812. c) (6 pnts) Can you describe how to find the inverse of A using characteristic equation? 2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above...
I quite weak at vector spaces. Can anyone tell me n
the reason behind it?
13:02 Previous Problem List Next (1 point) Determine whether the given set S is a subspace of the vector space V A, V = C2(1), and s is the subset of V consisting of those functions satisfying the differential equation y4y' 3y0 B. V2, and S is the set of all vectors (z1,2) in V satisfying 516r2 0 C. V, and S is the subset...
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