Question: Let x and y be vectors in Rn and define (a) Show that p ¥ z. Thus p is the vector projection of x onto

Let x and y be vectors in Rn and define

(a) Show that p Š¥ z. Thus p is the vector projection of x onto y; that is, x = p + z, where p and z are orthogonal components of x, and p is a scalar multiple of y.
(b) If ||p|| = 6 and ||z|| = 8, determine the value of ||x||.

peTyy and z=x-p

Step by Step Solution

★★★★★

3.32 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let In terms of these scalars we have p y and p T x Furth... 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)

949-M-L-A-E (683).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in. If ( is the angle between x and y, prove that the angle between Qx and Qy is also (. (This proves that the linear transformations...

Let x and y be vectors in an inner product space. Show that if x y then the distance between x and y is (||x||2 + ||y||2)1/2

Let A be an n n matrix and let x and y be vectors in Rn. Show that if Ax = Ay and x y, then the matrix A must be singular.

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...

Consider the plane, X, in R3 given by the 1Hector equation: x(s,t)= (l,l,2)+s(l,0,l)+t(l,l,0); 3,: E R. a} Compute a unit normal yector, n, to this plane. b} Define a linear transformation P : R3 }...

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...

Let u be a unit vector in R n , and let B = uu T .a. Given any x in R n , compute Bx and show that Bx is the orthogonal projection of x onto u, as described in Section 6.2. b. Show that B is a...

Given a unit vector qer", we saw in Homework 5, Exercise 5 that the nxn matrix Po = qq? orthogonally projects any vector xe R" onto the line spanned by q. Suppose now we have two mutually orthonormal...

5. Let W be a subspace of R" and W- := {x e R" : xy = 0 for all y E W } be its orthogonal complement. Since R" = WOW-, we may define P : R" -> R" by Pv = w where v = w + w with we W and w' E W-. We...

Let V and W be finite dimensional vector spaces. You may find problem 4 useful here . (a) (3 points) Suppose T : V - W satisfies rank? = 1. Show that there are vectors I E W and y E V so that T = y"....

What is a Bohr radius? What does it have to do with electronic transitions in semiconductor materials? What are Excitons?

Write an application for MBA submission essay. Briefly state why you wish to study for this degree (MBA), why you have chosen the University of Tex as in Tyler and specify what you hope to accomplish...

Which of the following best describes the risk - return trade - off? The assumption that all low - risk investments yield lower returns than high - risk investments. The principle is that investors...

For Activity A, the optimistic estimate is 10 days, the most likely estimate is 12 days, and the pessimistic estimate is 25 days. What is the PERT estimate and standard deviation? E = (10 + (4 * 12)...

In each case determine whether U is a subspace of R3. Support your answer. (a) U = {[1 s t]T | s and t in R}. (b) U = {[0 s t]T | s and t in R}. (c) U = {[r s t]T | r, s, and t in R, - r + 3s + 2t =...

If a1, a2,..., ak are nonzero scalars, show that span {a1X1, a2X2,..., akXk} = span{X1 ,X2,...,Xk) for any vectors X, in Rn.

Suppose that U = span {X1, X2,Xk} where each Xi is in Rn. If A is an m n matrix and AXi = 0 for each i, show that AY=0 for every vector Y in U.

3) Bond Valuation: Doisneau 19 year bonds have an annual coupon interest of 13%, make interest payment on a semiannual basis, and have a $1,000 par value. If the bonds are trading with a market's...

An investment will pay you $52,000 in 10 years. If the appropriate discount rate is 7.9 percent compounded daily, what is the present value? (Use 365 days a year. Do not round intermediate...

Question 20 2 points Save Answ Suppose a bank enters a repurchase agreement in which it agrees to sell Treasury securities to a correspondent bank at a price of $9999907 with the promise to buy them...