34. [M] Let B = {1, cos t, cos? t,...,cos t} and C = {1, cos t, cos 21,..., cos 6t}. Assume the following trigonometric identities (see Exercise 37 in Section 4.1). cos 2t =-1+2 cos? t cos 3t = -3 cos t +4 cos?t cos 4t = 1-8 cos?t + 8 cost cos 5t = 5 cost-20 cos' t + 16 cos t cos 6t = -1+ 18 cos? t-48 cos t +32 cos t Let H be the subspace of functions spanned by the functions in B. Then B is a basis for H, by Exercise 38 in Section 4.3. a. Write the B-coordinate vectors of the vectors in C, and use them to show that C is a linearly independent set in Н. b. Explain why C is a basis for H.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![34. [M] Let B = {1, cos t, cos? t,...,cos f} and C = {1, cos t,
cos 21, ..., cos 6t}. Assume the following trigonometric
identities (see Exercise 37 in Section 4.1).
%3D
cos 2t = -1+t 2 cos? t
cos 3t = -3 cos t +4 cos?t
cos 4t = 1-8 cos?t + 8 cost
cos 5t = 5 cost-20 cos' t +16 cos t
cos 61 = -1+ 18 cos? t-48 cos t +32 cos t
%3D
|
Let H be the subspace of functions spanned by the functions
in B. Then B is a basis for H, by Exercise 38 in Section 4.3.
a. Write the B-coordinate vectors of the vectors in C, and
use them to show that C is a linearly independent set in
Н.
b. Explain why C is a basis for H.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2Fee58e247-a979-4814-83a9-2d80c4cc6188%2Flcxeihc_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
