That the function f ( t ) = t 2 | t | , and g ( t ) = t 3 are linearly dependent on interval 0 < t < 1 and on − 1 < t < 0 .

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Answer 1

Question

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

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Page of 2 ZOOM + 1) Answer the following questions by circling TRUE or FALSE (No explanation or work required). i) If A = [1 -2 1] 0 1 6, rank(A) = 3. (TRUE FALSE) LO 0 0] ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations. (TRUE FALSE) iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE) iv) A set S of vectors in an inner product space V is orthogonal when every pair of vectors in S is orthogonal. (TRUE FALSE) v) Dot product of two perpendicular vectors is zero. (TRUE FALSE) vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE) 2) a) i) Determine which function(s) are solutions of the following linear differential equation. - y (4) — 16y= 0 • 3 cos x • 3 cos 2x -2x • e • 3e2x-4 sin 2x ii) Find the Wronskian for the set of functions that you found from i) as the solution of the differential equation above. iii) What does the result…

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1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11

Answer 2

Question

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

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Answer 3

Question

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

Expert Solution & Answer

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Answer 4

Question

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

Expert Solution & Answer

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Answer 5

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

Answer 6

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

Answer 7

Chapter 4.1, Problem 25P

(a)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

Answer 8

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

Answer 9

(b)

To determine

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

Answer 10

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

Answer 11

(c)

To determine

To show: That the value of W(f,g)=0, on interval −1<t<1.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - Prob. 6P Ch. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 8P Ch. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 10P

That the function f ( t ) = t 2 | t | , and g ( t ) = t 3 are linearly dependent on interval 0 &lt; t &lt; 1 and on − 1 &lt; t &lt; 0 .

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval 0<t<1 and on −1<t<0.

To show: That the function f(t)=t2|t|, and g(t)=t3 are linearly dependent on interval −1<t<1.

To show: That the value of W(f,g)=0, on interval −1<t<1.

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Chapter 4 Solutions

That the function f ( t ) = t 2 | t | , and g ( t ) = t 3 are linearly dependent on interval 0 < t < 1 and on − 1 < t < 0 .