Prove that every line through the origin in R3 is a subspace of R3.

Question:

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:08 AM

See More Questions

(a) Show that the linear transformation defined by a 3 Ã 3 proper orthogonal matrix corresponds to rotating through an angle around a line through the origin in R3-the axis of the rotation....
Let L R2 be a line through the origin in the direction of the unit vector u. (a) Prove that the matrix representative of reflection through L is R = 2uuT - 1. (b) Find the corresponding formula for...
Let L be the line through the origin in R2 with direction vector = [a b]T 0. If PL denotes projection on L, show that PL has matrix 1 ab a +b ab b - u
In Problems 1158, perform the indicated operation, and write each expression in the standard form a + bi. 2 + i i
The condensed balance sheet and income statement data for Symbiosis Corporation are presented below. Additional information: 1. The market price of Symbiosis common stock was $5.00, $3.50, and $2.80...
An enthalpy-concentration diagram is given in Figure for a mixture of n-hcxanc (H). and n-octane (0) at 101 kPa. Using this diagram, determine the following: (a) The mole-fraction composition of the...
A lot of compensation information is available to employees today on the Web (e.g., www.salary.com), and much of it is inaccurate. How can an organization assure employees that they are fairly...
During 2017, the following transactions were recorded by the Port Hudson Community Hospital, a private sector not-for-profit institution. 1. Gross charges for patient services, all charged to Patient...
Draw a graph of a function y = f(x) that satisfies all of the limits below. (a) lim f(x)=0 z-1- (b) lim f(x)=-2 z+1+ (c) lim f(x)=5 0+
Are the following functions analytic? Use (1) or (7). f(z) = Arg 2z
Let A be a skew - symmetric n n matrix. (a) Prove that xT Ax = 0 for all x in Rn. (b) Prove that I + A is invertible.
Let TA : R2 R2 be the matrix transformation corresponding to Find TA (u) and TA (v), Where And 2 2 LI 2
Mr. Larry Leininger donated $3,000,000 to a nongovernment VHWO on June 17, 20X8. 1. Assume that no restrictions are placed on the use of the donated resources. a. Prepare the required June 17, 20X8,...
A sample of 75 concrete blocks had a mean mass of $38.3 \mathrm{~kg}$ with a standard deviation of $0.6 \mathrm{~kg}$. a. Find a 95\% confidence interval for the mean mass of this type of...
It is desired to check the calibration of a scale by weighing a standard 10 -gram weight 100 times. Let $\mu$ be the population mean reading on the scale, so that the scale is in calibration if...
The article "Prediction of Performance and Evaluation of Flexible Pavement Rehabilitation Strategies" (K. Lee, K. Wilson, and S. Hassan, Journal of Traffic and Transportation Engineering,...
Refer to the data set lung.csv. The median ozone for all individuals in the study is 32.48. Can you conclude that people whose ozone exposure is greater than the median are more likely to have asthma...
The time taken by an automobile mechanic to complete an oil change is random, with mean 29.5 minutes and standard deviation 3 minutes. a. What is the probability that 50 oil changes take more than...
Barney Laron Ronnie OFallon died intestate on May 3, 1997, and was survived by three children. His oldest son, appellant William Martin OFallon, was appointed administrator of the estate * * * and,...
Les has collected stamps in his spare time for years. He purchased many of his stamps at a price much lower than the current market value. Les recently lost his job as a carpenter. Since his wife...
Either a generator matrix G or a parity check matrix P is given for a code C. Find a generator matrix G ¥ and a parity check matrix P ¥ for the dual code of C. 1 0 1 1 P = 0 1 0 0 Lo
Find generator and parity check matrices for the dual of the (7, 4) Hamming code in Example 3.71. The even parity code E n is the subset of Z n 2 consisting of all vectors with even weight. The...
(a) Find generator and parity check matrices for E 3 and Rep 3 . (b) Show that E 3 and Rep 3 are dual to each other.
Write a program that accepts a phone number of the form +1(xxx)-XXX-XXXX where x is a digit, and displays the sum of all digits in the phone number. Example (user's input in red, output in blue)...
4. (25 points) The reverse of a directed graph G is another directed graph GR with the same vertex set with the property that if (u, v) is an edge in G then (v, u) is an edge in GR. Consider the...
2. (25 points) The Fibonacci numbers Fo, F1,..., are defined by Fo 0, F11, Fn = Fn-1 + Fn-2 Use induction to prove that: (a) Use induction to prove that Fn 20.5n for n 6 (b) Use induction to prove...

Prove that every line through the origin in R3 is a subspace of R3.

Question:

Step by Step Answer:

If a line l passes through the origin then it has the eq...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions