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)

Expert Solution

Colby Messinger answered 2 years ago

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|

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) = 2e2x, f2(x) = 4e4x, f3(x) = 8e8x (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

T or F 1) Any N vectors spanning R^n are linearly independent 2)R5 has 7 linearly...

T or F 1) Any N vectors spanning R^n are linearly independent 2)R5 has 7 linearly independent vectors 3) If a set of vectors with n elements is linearly dependent, then a set with n - 1 elements is also linearly dependent 4) There exists a Linear Function T:R^n -> R^n such that the range and the kernel of T are equal. 5) If a vector space has a dimension of n, then a basis for the vector space will...

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)

Determine whether the members of the given set of vectors are linearly independent. If they are...

Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0

2. Find all eigenvalues and corresponding linearly independent eigenvectors of A = [2 0 3 4]...

2. Find all eigenvalues and corresponding linearly independent eigenvectors of A = [2 0 3 4] (Its a 2x2 matrix) 4. Find all eigenvalues and corresponding linearly independent eigenvectors of A = [1 0 1 0 2 3 0 0 3] (Its's a 3x3 matrix) 6. Find all eigenvalues and corresponding eigenvectors of A =    1 2 3 0 1 2 0 0 1    .(Its a 3x3 matrix)

Are {4cos^2(x),cos(2x),5} linearly independent? prove without wronskian

Find the Laplace transform of the following functions: a. p(t) = 6[u(t − 2) − u(t...

Find the Laplace transform of the following functions: a. p(t) = 6[u(t − 2) − u(t − 4)] b. g(t) = (4 + 3e−2t)u(t) c. h(t) = 2r(t) − 2r(t − 2)

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)}

In the following examples, indicate whether you would perform a t-test of independent means or a...

In the following examples, indicate whether you would perform a t-test of independent means or a dependent means (5 POINTS) Two groups of older adults were given different levels of a treatment for arthritis pain. Which treatment was more effective? A health care provider wanted to know whether his patients who received additional in-home care recovered more quickly than those who received the standard amount of in-home care One group of 85 year olds were provided an exercise program for...

Question