34. [M] Let B D f1; cost; cos2 t; : : : ; cos6 tg and C D f1; cost; cos 2t; : : : ; cos 6tg. Assume the following trigonometric identities (see Exercise 37 in Section 4.1). cos 2t D 1 C 2 cos2 t cos 3t D 3 cost C 4 cos3 t cos 4t D 1 8 cos2 t C 8 cos4 t cos 5t D 5 cost 20 cos3 t C 16 cos5 t cos 6t D 1 C 18 cos2 t 48 cos4 t C 32 cos6 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 H. b. Explain why C is a

b

8(4)^8=72^feet to say that the total can conclude to 8(4) which as you know would mean 8 x 4. that equals 32w. 32^ could make a 72 answer as well. but your coefficent will remain w so your answer is 72w.

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option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0