Question: Prove that for any vectors u, v, and w in R2 or R3 and any scalar c, we have (a) (u + cv) w

Prove that for any vectors u, v, and w in R2 or R3 and any scalar c, we have
(a) (u + cv) ∙ w = u ∙ w + c(v ∙ w);
(b) u ∙ (cv) = c(u ∙ v);
(c) (u + v) ∙ (cw) = c(u ∙ w) + c(v ∙ w).

Step by Step Solution

★★★★★

3.55 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a u cv w u w cv w u w c... 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)

951-M-L-A-L-S (6992).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Provide reasons (mostly vector space properties) as justification for each of the seven steps of the following proof. Theorem For any vectors u, v, w Cm, if u + v = u + w, then v = w. Proof: Let u,...

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. For any vectors u, v, and w in V 3 , (u + v)...

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...

Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans 8a + 3b W, or give an example or an explanation...

How would you answer these? Question 1 (1 point) Which of the following vectors is not perpendicular to vector u =(-5, 2, 1)? O al v = (3, 7, 1) Obj v = (-2, -10, 10) O cv= (1, 2, 1) O d) v= (4, 5,...

. Leave no spaces between mathematical operators. For example, the line 2x + 5y = 10 should be typed in as "2x+5y=10." . Do not begin your solution with an equal sign. For example, the answer to the...

Mark each of the following statements true or false: (a) For vectors u, v, and w in Rn, if u + w = v + w, then u = v. (b) For vectors u, v, and w in Rn, if u w = v w, then u = v. (c) For vectors u,...

90. 86-91. Using gradient rules Use the gradient rules of Exercise 85 to find the gradient of the following functions.90. f(x, y, Z) = (x + y + z)exyz85. Rules for gradients Use the definition of the...

Assume that u, v, and w are vectors in R 3 that form the sides of a triangle (see figure). Use the following steps to prove that the medians intersect at a point that divides each median in a 2:1...

a) b) In this assignment, you are going to evaluate the recent investment performance for two stocks of your choice relative to the FBMKLCI (use FBMKLCI historical prices as attached). i. ii. iii....

The following transactions occurred during March 2016 for Wainwright Corporation. The company owns and operates a wholesale warehouse. 1. Issued 44,000 common shares in exchange for $440,000 in cash....

You have been offered a unique investment opportunity. If you invest $ 2 5 comma 0 0 0 today , you will receive $ 1 comma 2 5 0 one year from now, $ 3 comma 7 5 0 two years from now, and $ 2 5 comma...

You are the project manager of the Carpet Installation Project for a new building. Your BAC is $600,000. You have spent $270,000 of your budget. You are now 40 percent done with the project, though...

Find the intercepts of 5x - 2y = -10 and graph the line.

Find the slope and the y-intercept of the line with equation -3x + 2y = 5.

Clear Signal charges $80 for a cell phone and $49.95 per month under its standard plan. Write an equation that can be used to determine the total cost C(t) of operating a Clear Signal cell phone for...

Question 1 Although its own operations have shown no growth over the past decade, Hammerworks Inc. has built up a significant cash balance ($2.9 billion) in anticipation of a collapse in equity...

Find the following values. Compounding/discounting occurs annually. Do not round Intermediate calculations. Round your answers to the nearest cent. a. An initial $200 compounded for 10 years at 10%....

DISCUSS QUESTION #4 Apollo Inc paid a dividend last year of $1.50. Dividends are expected to grow at a rate of 17% this year, 15% next year, 10% the following year and 5% thereafter. The required...