Question: Prove: If u, v, and w are vectors in Rn and k is any scalar, then (a) u (kv) = k(u v) (b)

Prove: If u, v, and w are vectors in Rn and k is any scalar, then
(a) u ∙ (kv) = k(u ∙ v)
(b) u ∙ (v + w) = u ∙ v + u ∙ w

Step by Step Solution

★★★★★

3.30 Rating (147 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Prove If u v and w are vectors in R n and k is any scalar then a u kv ku v b ... 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

938-M-L-A-E (1209).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If u, v, and w are vectors in R n , n 2, and c is a scalar, explain why the following expressions make no sense: (a) u v (b) u v + w (c) u (v w) (d) c (u + w)

Q:

In Exercises 1-3, suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 5, (v, w) = 0 ||u|| = 1, ||v|| = 3, ||w|| = 2 Evaluate the expressions in Exercises...

Q:

Suppose that u, v, and w are vectors in an inner product space such that {u, v} = 1, {u, w} = 5, {v, w} = 0 ||u|| = 1, ||v|| = 3, ||w|| = 2 Evaluate the expressions ||2u - 3v + w||

Q:

Let u , v , and w be vectors, and let c be a scalar. Prove the given property. (utv) . w = u . W +v. W Let u = (U1, U2), v = (V1, V2), and w = (w1, w2). Then ( u + v ) . w = ( 41, U2) + ( v1, v2) ) ....

Q:

Prove parts (a) and (d), of Theorem 6.1.1, justifying each step with the name of a vector space axiom or by referring to previously established results. Theorem 6.1.1 If u, v and w are vectors in a...

Q:

17 Consider the system below. Which of the following describes the intersection of the three planes if k = 0? 1 3 0 0 1 -2 -1 O 0 k 2 Select one alternative: O A single point. O A common line. O...

Q:

C webassign.net/web/Student/Assignment-Responses/submit?dep=3 YouTube Maps Find the cross product of the unit vectors. j xi Sketch your result. K O O K O 750 F Cloudy Q Search LCourse Hero X Content...

Q:

4.1 Questions 10,17,21,22 No plagrism and please write on paper thank you! 10. The set of all real-valued functions f defined everywhere on the real line and such that f(1) = 0 with the operations...

Q:

i need help with these, thank you 1.20 (Challenge) Magnitude of the vector v. Show work. (Section 2.9) Knowing the angle between a unit vector i and unit vector j is 120, calculate a numerical value...

Q:

Calculus 3 Section 12.4 Reading Assignment: The Cross Product Answer Only Exercise 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very carefully...

Q:

Refer to the information for Kinsella Seed above. What journal entry should be recorded on December 31, 2011? a. Debit Interest Expense 5,000; credit Interest Payable 5,000. b. Debit Interest...

Q:

A high-volume printer produces minor print-quality errors on a test pattern of 1000 pages of text according to a Poisson distribution with a mean of 0.4 per page. (a) Why is the number of errors on...

Q:

Assess the impact of macroenvironmental factors on the likely level of enrollment at your university over the next decade. What are the implications of these factors for the job security and salary...

Q:

Have all of the project sponsors been considered? If so, what is the risk that the project will not be approved by the appropriate sponsors within the participating organizations?

Q:

Span {u, v} for all h and k. Let u= and v=12 Show that is in

Q:

In Exercises 1 and 2, mark each statement True or False. Justify each answer. 1. a Another notation for the vector b. The points in the plane corresponding to And Lie on a line through the origin. c....

Q:

Denote the columns of A by a1, a2, a3, and let W = Span {a1, a2, a3}. Let And a. Is b in {a1, a2, a3}? How many vectors are in {a1, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a1...

Q:

Bond P is a premium bond with an 7.4 percent coupon, a YTM of 6.15 percent, and 15 years to maturity. Bond D is a discount bond with an 7.4 percent coupon, a YTM of 9.15 percent, and also 15 years to...

Q:

Teeswater Corp. shows the following information on its 2 0 2 0 statement of comprehensive income: sales = $ 2 4 2 , 0 0 0 ; costs = $ 1 4 6 , 0 0 0 ; other expenses = $ 8 , 4 0 0 ; depreciation...

Q:

Using Rstudio We will use a logistic regression to predict the probability ofdefaultusing income andbalanceon theDefaultdata set in the ISLR package. We will now estimate the test error of this...