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

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

Step by Step Solution

★★★★★

3.51 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

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

blur-text-image
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)

Word file Icon

859-L-A-L-S (2436).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(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....

Q:

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...

Q:

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

Q:

In this exercise, you will be given two matrices A and B. You will write a set of commands in MATLAB that determine whether Row A and Row B are subspaces of the same space R". If yes, your code has...

Q:

(a) Show that a line t 0 through the origin of R3 is a subspace of R3. (b) Show that a line t in R3 not passing through the origin is not a subspace of R3.

Q:

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...

Q:

for part 5 chose one a or b 1. The following matrices are related. A' is row-equivalent to A, and A" is the transpose of A. Use this information to complete the following: N 2 1 -6 00 Co its co 3 A =...

Q:

ool rank of a matrix import Pkg. add (RowEchelon) using (Row Echelon) using (LinearAlgebra) rank A) syntax: extra token ""after end of expression 2) Determine whether or not Col(A) and Col(B) are the...

Q:

question # 15 only DeEl howard-anton-chris-rorres-elementary-linear-algebra-applications-version-11th-edition.pdf X 4.2 Subspaces 201 (b) All sequences v in R" of the form origin only. If it is a...

Q:

In each part, the solution space is a subspace of R3 and so must be a line through the origin, a plane through the origin, all of R3 or the origin only. For each system, determine which the case is....

Q:

one liter saturated solution of AgCl [Ksp = 1.6 x 10-10], 0.1 mol of CuCl [Ksp = 1.0 x 10-10 ] is added. The resultant concentration of Ag+ in the solution is 1.6 10-x. The value of x is ___.

Q:

A player hits an overhead smash at full arm extension at the top of his racquet, which is 7 feet from the ground. The ball travels 16.3 feet (ignore the effects of gravity). Consult the following...

Q:

Can you use the annual revenues generated by National Basketball Association (NBA) franchises to predict franchise values? Figure 2.14 on page 94 shows a scatter plot of revenue with franchise value,...

Q:

Why do all of the tests you did have the same number of degrees of freedom for the hypothesis of no association between dzgroup and totcst?

Q:

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

Q:

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...

Q:

(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.

Q:

Freight Train Construction is analyzing a proposed project. The company expects to sell 1 , 4 0 0 units, + - 2 percent. The expected variable cost per unit is $ 2 1 0 and the expected fixed costs are...

Q:

A research institute reports that 69% of workers reported that theyand/or their spouse had saved some money for retirement. Complete parts a and b below. a.If a random sample of 40 workers istaken,...

Q:

Werth Company produces tie racks. The estimated fixed costs for the year are $288,000, and the estimated variable costs per unit are $14. Werth expects to produce and sell 60,000 units at a price of...