Question: Determine whether the given functions are linearly independent or linearly dependent: (a) 2 - x2, 3x, x2 + x - 2 (b) 3x - 1,

Determine whether the given functions are linearly independent or linearly dependent:
(a) 2 - x2, 3x, x2 + x - 2
(b) 3x - 1, a (2 a + 1), jc (a- - 1)
(c) ex, ex+1
(d) sin x. sin(A + 1)
(e) ex,ex+l,ex+2
(0 sinx, sin(x-+1). sin(x + 2)
(g) ex,xex,x2ex
(h) ex, e2x. e3x
(i) x+.y, x-y+1, a+3y+2 -these are functions of two variables.

Step by Step Solution

★★★★★

3.49 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Linearly dependent b Linearly independent ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (1838).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

(a) Verify that the given functions are linearly independent and form a basis of solutions of the given ODE. (b) Solve the IVP. Graph or sketch the solution. y'' + 0.6y' + 0.09y = 0, y(0) = 2.2,y'...

(a) Verify that the given functions are linearly independent and form a basis of solutions of the given ODE. (b) Solve the IVP. Graph or sketch the solution. x 2 y'' - xy' + y = 0, y(1) = 4.3, y' (1)...

(a) Prove that the polynomials i = 1.........k, are linearly independent if and only if the k (n + 1) matrix A whose entries are their coefficients aij ,1 i k, 0 j n. has rank k. (b) Formulate a...

Please give very thorough explanations for all the questions, thank you 1. Find the differential equation which describes the family of curves y? = c1 (I + 1). 2. Classify the following differential...

Please show all work and give explanation for question 1-3, thank you very much 1. Find the differential equation which describes the family of curves y? = c1 (I + 1). 2. Classify the following...

solve number 17 In Problems 15-22 determine whether the given functions are linearly inde- pendent or dependent on (-co, co). 15. fi(x) = x, f2(x) = x2, f3(x) = 4x - 3x2 16. f (x) = 0, f2(x) = x,...

Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem Question list K below. y'"' - vx+ 1y = sin x, y(n) = 9,...

Use the Wronskian to determine if the given functions are linearly independent on the indicated interval. f(x) = 19, g(x) = x, h(x) =3x ; the real line Select the correct choice below and, if...

Determine whether the given functions are linearly dependent or linearly independent on the specified interval Justify your decision x 1 2 on 0 00 CEEEH Select the correct choice below and if...

Do Homework - Homework 6.1 Basic Theory of Linear Diff. Eq. - Google Chrome mathxl.com/Student/PlayerHomework.aspx?homeworkld=599185316&questionld=2&flushed=true&cld=6535730¢erwin=yes Fall 2021...

10. "Labor has had huge success in its political efforts since the merger." Do you agree or disagree?

The diameter of cotter pins produced by an automatic machine is a characteristic of interest. Based on historical data, the process average diameter is 15 mm with a process standard deviation of 0.8...

The total dollar return on a stock is the sum of the Blank _ _ _ _ _ _ and the Blank _ _ _ _ _ _ . Multiple choice question.

Japan suffered throughout the 1990s and into the 2000s from the after-effects of an asset price bubble that burst in 1990. The asset price bubble was caused by excessive money growth in the late...

Let A be a 3 3 matrix and suppose that 2a1 + a2 - 4a3 = 0 How many solutions will the system Ax = 0 have? Explain. Is A nonsingular? Explain.

Let A be a 3 3 matrix and suppose that a1 = 3a2 - 2a3 Will the system Ax = 0 have a nontrivial solution? Is A nonsingular? Explain your answers.

Let A and B be n n matrices and let C = AB. Prove that if B is singular then C must be singular.

1 (25 points) Use the Hermes dataset to answer these questions: For black (color category) bags, is the average hammer price higher for matte or shiny finishes? Hint: Use the Text to Columns feature...

Using the following data for First Bank: a) Calculate the banks static funding GAP over the various time buckets (0-6 months, 6 months - 1 year, and over 1 year). Consider both the periodic GAP and...

OE Question 24 1 pts 24. The bonds issued by General Motors was recently downgraded by both Moody's and Standard and Poor's to Junk bond status. As a result, the entire auto industry was adversely...