Question: Show that {u 1 , u 2 } or {u 1 , u 2 , u 3 } is an orthogonal basis for R 2

Show that {u1, u2} or {u1, u2, u3} is an orthogonal basis for R2 or R3, respectively. Then express x as a linear combination of the u's.


U = [] = [-] and x = [ - ] -4

U = [] = [-] and x = [ - ] -4 3 U12 6

Step by Step Solution

★★★★★

3.29 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Data from in Theorem 4 Data from in Theorem 5 Since u U 66 0 u... 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

Students Have Also Explored These Related Linear Algebra And Its Applications Questions!

Q:

Show that {u 1 , u 2 } or {u 1 , u 2 , u 3 } is an orthogonal basis for R 2 or R 3 , respectively. Then express x as a linear combination of the u's. 2 --------] = 2 = = 4 0 4 and x = 3 7

Q:

Show that {u 1 , u 2 } or {u 1 , u 2 , u 3 } is an orthogonal basis for R 2 or R 3 , respectively. Then express x as a linear combination of the u's. --0--0--0--0 = 2 and = 4 4 6 4

Q:

Show that {u 1 , u 2 } or {u 1 , u 2 , u 3 } is an orthogonal basis for R 2 or R 3 , respectively. Then express x as a linear combination of the u's. 2 = [-] = [2], and x = [-2] 12 -3 -7

Q:

Question 1. (a) Assume that v1, ..., Un is an orthogonal basis of R" and that 7 ( R" satisfies U . 01 = 0, . ... U . Un = 0 Show that 7 = 0. (b) Assume that 71, ..., up is any basis of a subspace H...

Q:

Need Solution ASAP This assignment contains some TRUE or FALSE statements. For each statement you need to decide if it is true or not, and justify your answer. How to justify your answer. 0 In order...

Q:

Let n be even and A R nn be constructed from the vectors c, d R n as ai,i = di , ani+1,i = ci for i = 1, . . . , n, and ai,j = 0 otherwise. (a) Write a function that, given the vectors d, c R n ,...

Q:

Here are definitions of sequences and trees with integer elements: type iseq = Nil | Cons of int * (unit -> iseq) type itree = Leaf of int | Branch of itree * itree (a) In an ascending sequence such...

Q:

Please solve the problems attached below: . Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of the standard unit vectors. 3? + 4} 3E+33 A. B. C. 534} D....

Q:

Please do the following questions handwritten 6. Consider the ellipse 12 6 (a) Show that the point P(x, y) = (-V6, v3) lies on the ellipse. (b) Write down parametric equations that define the ellipse...

Q:

6.3.5 Verify that fu, ,u2) is an orthogonal set, and then find the orthogonal projection of y onto Span fu, , u23. 5 y = 14 1 , u, = 1 8 2 2 To verify that fu, ,u2) is an orthogonal set, find u, ....

Q:

Moming Star Ltd was registered on 1 July 2018, as a company with a constitution limiting the shares that could be offered to 7 000 000 Ordinary shares (including all classes) and 2 000 000 preference...

Q:

The following table gives the frequency distribution of the number of telephones owned by a sample of 50 households selected from a city. Number of Telephones Owned Frequency 0 3 1 21 2 15 3 5 4 6 a....

Q:

True or False. Typically the volume of grain traded on Futures Exchanges is far less than the physical amount of grain produced over a crop year True False Clear selection

Q:

Why is it important for managers to write grammatically correct language?

Q:

Consider the circuit in Example 2-34. Assume that devices fail independently. What is the probability mass function of the number of device failures? Explain why a binomial distribution does not...

Q:

Consider the time to recharge the flash in cell-phone cameras as in Example 3-2. Assume that the probability that a camera passes the test is 0.8 and the cameras perform independently. What is the...

Q:

Consider the patient data in Example 2-8. Suppose that patients are randomly selected with replacement from the total for hospital 4. What is the smallest sample size needed so that the probability...

Q:

Randall Sports has collected the following information over the last six months. Month Units produced Total costs March 10,000 $25,600 April 12,000 26,200 May 18,000 27,600 June 13,000 26,450 July...

Q:

McCormick & Company, is an American multinational food company who manufactures, markets, and distributes spices to the food industry in 160 countries. With regards to its financial performance for...

Q:

Hodge Inc. has some material that originally cost $74,600. The material has a scrap value of $57,400 as is, but if reworked at a cost of $1,500, it could be sold for $54,400. What would be the...