Question: Let u , v , and w be vectors, and let c be a scalar. Prove the given property. (utv) . w = u .

Let u, v, and w be vectors, and let c be a scalar. Prove the given property.

a scalar. Prove the given property. (utv) . w = u .

(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) ) . (w1, w2) = . ( W1 , W2 ) = UjW1 + viw1+ = UjW1 + U2w2 + = (U1, U2) . + ( v 1 , V 2 ) . =U . W +v . W

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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 Mathematics Questions!

- Symbolic functions must be entered using notation similar to the examples given below. - Do NOT include the name of the function or an equal sign. {i.e., do NOT include anything like '1' =' in your...

hello I need help solving those questions please 'Oblem # 1: Let P be the point (3, 2, -6). Suppose that the point P0(4, 1, 6) is % of the way from P to Q. Find the point Q. Problem #1: Enter the...

1. Let u = , v = , and w = be vectors. Find the indicated expression. U . V 2. Let A = (2, -1), B = (3, 1), C= (-4, 2), and D = (1, -5). Find the component form and magnitude of the vector. AC+ BD 3....

prove and please explain it with steps is a basis for V and a and o are flonzero scalars, then both fu and {au, bu} are also bases for V. 12. Let u, v, and w be distinct vectors of a vector space V....

I am stuck on this problem. How can I resolve this? Results for this submission Entered Answer Preview Result Let u, v, and w be arbitrary vectors in V. 2 Assume u + w = v + w. Adding -w to both...

Let u, v, w, z be vectors in R. (a) Compute the angle between 7 = (-2, 1, 1) and w = (1, 1, -2). (2 points) (b) Let u, v, u be vectors such that 1 and u 1 w. Find a vector such that Z v, w but u Z....

Questions. (1) mmarks) True or False? Justify your answer. Answers without correct justification will receive {0 credit. (3) Let u, v and W be nonzero vectors in R3. If u and v are each orthogonal to...

\fGiven: H is the orthocenter of 4ABC; P, Q, and R are the midpoints of AB,AC, and BC; U, V , and W are the midpoints of AH, CH, and BH. Prove thatP, Q, R, U, V , and W all lie on a common circle....

Let u, v and w be the vectors in R given by u = 5[0, -2, 5] + 4[-1, -1, 1], v= 5[0, -2, 5] - 3[-1, -1, 1], and w = -7u + 5v. Write w as a linear combination of [0, -2, 5] and [-1, -1, 1]. W= [0, -2,...

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...

Consider the function below. (If an answer does not exist, enter DNE.) F(x) : 9 - X = X (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease....

As in Section 5.4, assume that bonds pay a real return of 2 percent. Stocks pay 22 percent half the time and -6 percent half the time. Suppose you initially have wealth of $100, and let X be your...

What are the key steps involved in inventory management process?

Inspectors general are to keep arm's length from the agency head and not discuss problems and deficiencies relating to the administration of agency programs and operations with her or him. Group of...

How, and to what extent, do you think the problems experienced by BP in the Gulf of Mexico were related to organisational size and structure?

Explain the nature of power and management control, and review perspectives of organisational power;

Detail different forms of control and characteristics of an effective control system;