Question: (a) Prove that form an orthonormal basis for R3 for the usual dot product. (b) Find the coordinates of v = (1, 1, 1)T relative

(a) Prove that

form an orthonormal basis for R3 for the usual dot product.
(b) Find the coordinates of v = (1, 1, 1)T relative to this basis.
(c) Verify formula (5.5) in this particular case.

48-65 43 23 1-3 3.5 0 4.5

Step by Step Solution

★★★★★

3.52 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a We compute v 1 v 2 v 1 v 3 v 2 v 3 0 a... 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)

952-M-L-A-E (2201).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let (a) Show that {u1, u2, u3} is an orthonormal basis for R3. 1 1-0 LI

Verify that the vectors Form an orthonormal basis for R3 with the Euclidean inner product; then use Theorem 6.3.1 to express each of the following as linear combinations of v1, v2, and v3. (3, -7, 4)...

Use the Gram-Schmidt process to determine an orthonormal basis for R3 starting with the following sets of vectors: (a) (b) (c) 101 011 110 231 450 3

3. a Check if the three points (1, 2, 3). (4. 9. 1). (5, 2, 6) in R$ form an acute angle triangle. Inner product on R3 is the usual dot product. b) Let A = and B = 4 Show that whatever be x, A and B...

1. (5 pts) Let u=(U1, Uz) and V=(V1, V2) be vectors in R? under traditional vector addition and scalar multiplication. Is the following operation an inner-product? March through the 4 axioms listed...

(a) Show that v1,... , vn form an orthonormal basis of Rn for the inner product (v, w) = vT K w for K > 0 if and only if AT KA = I where A = (v1, v2 . . . vn). (b) Prove that any basis of Rn is an...

2 please explain it a, b, and c 2. In each part, apply the Gram-Schmidt process to the given subset S of the inner product space V to obtain an orthogonal basis for span(S). Then normalize the...

Chapter 7.1 Write on paper for upvote. questions: 1, 3 , 5, 11, 12, 26 please -145 -1455 - 1450 H O O HIN O HIN -NO InNo -No (6) HIN #ND HID Into O O a. for every vector x in R". As a first step in...

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...

3 Systems of differential equations Theorem 3. Any n linearly independent vectors in an n dimensional space V must also span V. That is to say, any n linearly independent vectors in an n dimensional...

A gym owner is considering opening a location on the other side of town. The new facility will cost $1.47 million and will be depreciated on a straight-line basis over a 20-year period. The new gym...

The figure below shows three vectors of lengths A = 63.9, B = 39.1, and C = 46.7. The angles are 8, = 29 and en = 56.9o, and C points along the negative y-axis. Determine the length of the vector A -...

14. The Fed Is a Money Machine Why is the Fed both literally and figuratively a money machine?

Which of the following AR processes are stationary, and why? 1, Xt = 1.10Xt1 + et 2, Yt = 0.70Yt1 + 0.10Yt2 + et 3, Zt = 0.80Zt1 + 0.30Zt2 + et 4, Wt = 0.80Wt1 + 0.30Wt2 + et Process (1) above is not...

Let u1 = (1 - i, i, 0), u2 = (2i, 1 + i, 1), and u3 = (0, 2i, 2 - i). Find scalars c1, c2 and c3 such that c1u1 + c2u2 + c3u3 = (- 3 + i, 3 + 2i, 3 - 4i).

Prove: If u and v are vectors in complex Euclidean w-space, then u (kv) = (u v)

Establish the identity for vectors in complex Euclidean n-space. |u i|* IV

The present value (at t=0 ) of the following cash flow stream is $6000 when discounted at 11% annually. That stream consists of payments made at the end of each of four periods. One of the payments,...

2. The BIG Corporation issued 12-year bonds on 10 Feb 2010. Each of these bonds has a face value of $10,000 and they are currently trading at a yield of 11.50% per annum. The bonds pay quarterly...

Problem 10-14 NPV Break-Even Analysis (LO3) 20 points Modern Artifacts can produce keepsakes that will be sold for $70 each. Nondepreciation fixed costs are $2,000 per year, and variable costs are...