Question: Let a, b Rm, b 0, and set (0 = a + tb. Show that C = (R) is a smooth unbounded curve

Let a, b ∈ Rm, b ≠ 0, and set ɸ(0 = a + tb. Show that C = ɸ(R) is a smooth unbounded curve which contains a and a + b. Prove that the angle between ɸ(t1) - ɸ(0) and ɸ(t2) - ɸ(0) for any t1, t2 ≠ 0 is 0 or π.

Step by Step Solution

★★★★★

3.48 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Since t a 0 C is smooth Since ta x 0 ua x 0 impl... 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)

741-M-N-A-D-I (746).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Let A Rmn, b Rm, and let x0 be a particular solution to the system Ax = b. Prove the following. A vector y in Rn will be a solution to Ax = b if and only if y = x0 + z, where z N(A). If N(A) =...

Let A be an m n matrix with m > n. Let b Rm and suppose that N(A) = {0}. (a) What can you conclude about the column vectors of A? Are they linearly independent? Do they span Rm? Explain. (b) How...

Let A be an m x n matrix, let P be the projection matrix that projects vectors in Rm onto R(A), and let Q be the projection matrix that projects vectors in R" onto R(AT). Show that (a) I - P is the...

1. Consider the two points x 1 = (1, 1), x 2 = (1, 0) in R2 . Draw the set of points which can be obtained by using the following operations. (a) x = 1x 1 + 2x 2 , 1, 2 R (linear combination) (b) x =...

Steel manufacturing in the US requires only one input: labor. Steel is produced by a representative rm under perfect competition according to the production function 1 L = L St ) 2 Throughout this...

Let the equations of two lines en a plane be y=ax+b, y=ex+d. where a 5-3 U, c % . Prove that, if the two lines. are perpendicular to each other, then m: = l. Let a, b, c E R' be linearly independent...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

2. Let a,b E Rm, b f 0, and set 1>(t) = a + tb. Show that G = 1>(R) is a smooth unbounded curve that contains a and a + b. Prove that the angle between 1>(tI) -1>(0) and 1>(t2) -1>(0) for any tI, t2...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

soth a. On December 31, 2018, ABC Partnership's Statement of Financial Positions shows that A, B and C have capital balances of P500,000, P300,000 and P200,000 with profit or loss ratio of 1:3:6. On...

What is information asymmetry, and how does it affect insurance companies?

a. Why are viral diseases more difficult to treat than bacterial diseases? b. You are a researcher aiming to develop a drug to reduce the multiplication of chickenpox (varicella zoster) virus....

The return statistics for two stocks are given below: ABC 1 Stock AStock B 2 Exp. return 0 . 0 6 0 . 0 8 8 3 Variance 0 . 1 1 5 6 0 . 0 7 2 9 4 St . dev . 0 . 3 4 0 . 2 7 5 Covariance 0 . 0 6 4 3 6...

Classroom assessment: Standard error. In the Ryan (2006) study described in Question 28, participants selected 120 samples of size 3 from a population of 5 scores (0, 0, 0, 3, and 6) using...

A byte is a sequence of eight bits and each bit is either 0 or 1. (a) How many different bytes are possible? (b) If the first bit of a byte is a parity check, that is, the first byte is determined...

In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the...

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a...

Your rich uncle just died and left you a nice gift in his will. You will receive $10,000 per year for five years starting next year. Eight years after that finishes, you will receive $5,000 per year...

what are some creative examples of a spontaneous generation, black holes, and gray holes? I have this information from my book but I'm kind of confused. Spontaneous generation. The APPLY INSURANCE...

Please help with question. Avoid question already bubbled in. 10) A college student is about to purchase a car when the salesman recommends that he should sign up for a protection plan. Under this...