Question: 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

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 - u²

1 ab a +b ab b - u

Step by Step Solution

★★★★★

3.36 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Write x y T Then Hence the matrix of P ... 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

950-M-L-A-L-S (6422).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let ¬ be the line through the origin in R2 with direction vector Use the method of Example 6.85 to find the standard matrix of a reflection in . dz

Q:

Let e be a line through the origin in R2, Pl the linear transformation that projects a vector onto l, and Fl the transformation that reflects a vector in l. (a) Draw diagrams to show that Fl is...

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:

Could you help me with these questions? The details are in the pictures provided below. We call this operator the orthogonal projection of R" onto the line. The standard matrix for this reflection is...

Q:

Linear Algebra Final answer only - No Explanation Section 4.2 Matrix of Transformations: Problem 7 :1 point: Find the malrix A of the linear transformation T from lit\" to R2 that rotates any...

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:

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

MATH 211 SPRING 2017, Assignment 3 (due Monday, Feb. 27 (A02) and Tuesday, Feb. 28 (A01) in class) Show your work clearly. Illegible or disorganized solutions may receive no credit. Note: A vector is...

Q:

7 (a) Let u = [3] E R2. Consider the linear transformation :R2> [R2 (ll-V V|> )u 11-\" u U where - denotes the dot product on R2. (Recall: l I] - [ I] = \"101 + 14202.) \"2 U2 Geometrically, this...

Q:

Structure factor of diamond the crystal structure of diamond is described Chapter 1. The basis consists of eight atoms if the cell is taken as the conventional cube.? (a) Find the structure factor S...

Q:

Instead of using the x- and y-axes of Fig. 4.8 to analyze the situation of Example 4.1, use axes rotated 37.0 counterclockwise, so the y-axis is parallel to the 250-N force. (a) For these axes find...

Q:

1. Explain the uses, limitations, and content of the statement of financial position.

Q:

Which of the following items is included in the calculation of GDP? a. Purchase of 100 shares of General Motors stock b. Purchase of a used car c. The value of a homemakers services d. Sale of Gulf...

Q:

The set of all real-valued functions f defined everywhere on the real line and such that f (1) = 0, with the operations defined in Example 4. In Exercise a set of objects is given, together with...

Q:

The set of all positive real numbers with the operations x + y = xy and kx = xk In Exercise a set of objects is given, together with operations of addition and scalar multiplication. Determine which...

Q:

Show that the following sets with the given operations fail to be vector spaces by identifying all axioms that fail to hold. (a) The set of all triples of real numbers with the standard vector...

Q:

Number of payments. Your grandfather will sell you a piece of beachfront property for $ 6 0 , 0 0 0 . He says the price is firm whenever you can pay him cash. You know your finances will only allow...

Q:

QUESTION 1 1) In a normal distribution find the proportion of area that is a) Less than a z-score of 1.52 b) in between the z-scores of -1.30 and 1.20 c) greater than a z-score of 1.89 2) In a normal...

Q:

Honorable Experts, ITS MY 5TH TIME POST, STILL I COULD NOT FIND A PROPER ANSWER, PLEASE SOLVE THIS ACCORDING TO MY ANSWER. I WOULD BE ALWAYS GRATEFUL TO YOU. could you please solve this with 100%...