Which of the following sets of functions are linearly independent on the interval (−∞, ∞)? (i) ...

Which of the following sets of functions are linearly independent on the interval (−∞, ∞)?

(i) f₁(x) = x, f₂(x) = 6x, f₃(x) = x² + 3

(ii) f₁(x) = 2e^2x, f₂(x) = 4e^4x, f₃(x) = 8e^8x

(iii) f₁(x) = 4sin²x, f₂(x) = 10cos 2x, f₃(x) = x

(A) (ii) only (B) (iii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) all of them (F) (i) and (ii) only (G) (i) only (H) none of them

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Determine whether the following pairs of functions are linearly independent or not on the whole real...

Determine whether the following pairs of functions are linearly independent or not on the whole real line. Determine whether the following pairs of functions are linearly independent or not on the whole real line. BEWARE: You only get 3 tries. Linearly dependent * 1. f(theta) = 14 cos 3theta and g(theta) = 56cos^3 theta - 42 cos theta. Linearly dependent 2. f(t) = t^2 + 14t and g(t) = t ^2 - 14t Linearly dependent 3.f(t)=t and g(t)=|t|

Check whether the following families of functions of t are linearly independent or not (a) t^2...

Check whether the following families of functions of t are linearly independent or not (a) t^2 + 1, 2t, 4(t + 1)^2 (b) sin(t) cos(t), sin(2t) + cos(2t), cos(2t) (c) e^2t , e^-2t , 2e^t (d) 2e^t , 3 cosh(t), 13 sinh(t) (e) 1/((t^2)-1) , 1/(t + 1), 1/(t-1)

How could these histograms associated with the following frequency sets be described? Frequency Class Interval I...

How could these histograms associated with the following frequency sets be described? Frequency Class Interval I II III IV 100 to <120 6 5 35 20 120 to <140 10 7 15 10 140 to <160 45 10 10 4 160 to <180 10 15 5 25 180 to <200 6 33 5 11 The histogram associated with frequency set I is ---Select--- Options (positively skewed negatively skewed bimodal multimodal symmetric .) The histogram associated with frequency set II is ---Select--- Options(...

1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1...

1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1 = {(1, 2, 3),(4, 5, 6),(6, 9, 12)}. (b) S2 = {(1, 2, 3, 4),(5, 6, 7, 8),(3, 2, 1, 0)}. (c) S3 = {(1, 2, 3, 4),(5, 6, 7, 8),(9, 10, 11, 12)}

Determine whether each set of vectors is linearly dependent or linearly independent. a) (1,1,0,1), (1,0,1,1), (0,1,1,1)...

Determine whether each set of vectors is linearly dependent or linearly independent. a) (1,1,0,1), (1,0,1,1), (0,1,1,1) b) (1,0,1,0), (0,1,0,1), (1,-1,1,-1), (1,-1,0,0)

i) A set of 4 6-tuples (“sextuplets”) is linearly independent: (always), (never), (sometimes). ii) A set...

i) A set of 4 6-tuples (“sextuplets”) is linearly independent: (always), (never), (sometimes). ii) A set of 6 4-tuples (“quadruplets”) is linearly independent: (always), (never), (sometimes). iii) A set of 4 equations with 6 unknown variables which is consistent has a unique solution: (always), (never), (sometimes). iv) A set of 4 equations with 6 unknown variables is inconsistent: (always), (never), (sometimes) v) A set of homogeneous equations is inconsistent: (always), (never), (sometimes) vi) The solution to a set of homogeneous...

Which of the following statements is/are FALSE? I YTM is the discount rate that sets the...

Which of the following statements is/are FALSE? I YTM is the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. II To calculate the expected return, one should discount promised payments. III To calculate the YTM, one should discount expected payments. IV If there is a risk of default, then the bond’s expected return is greater than the YTM. V The realized return is always equal to the...

1) a. Which of the following sets are the empty set? i. { x | x...

1) a. Which of the following sets are the empty set? i. { x | x is a real number and x2 – 1 = 0 } ii. { x | x is a real number and x2 + 1 = 0 } iii. { x | x is a real number and x2 = -9 } iv. { x | x is a real number and x = 2x + 1 } b. Let A = {1, 2, 3,...

Two linearly independent solutions of the following equation (1 − x) y″ + x y′ − ...

Two linearly independent solutions of the following equation (1 − x) y″ + x y′ − y = 0 are y1(x) = 4ex and y2(x) = 8x. (a) Find the Wronskian W(y1, y2) of y1 and y2. (b) Using the method of variation of parameters, find a particular solution of (1 − x) y″ + x y′ − y = 2(x − 1)2 e −x

Which of the following sets are closed under addition? (i) The set of all vectors in...

Which of the following sets are closed under addition? (i) The set of all vectors in R2 of the form (a, b) where b = a2. (ii) The set of all 3 × 3 matrices that have the vector [3 -1 -1]T as an eigenvector. (iii) The set of all polynomials in P2 of the form a0 + a1 x + a2 x2 where a0 = a2. (A) (i) only (B) all of them (C) (ii) only (D) (i) and...

Subjects