Consider the inner product on R2 defined by ((x1, x2), ( Y2)) = x14 + 4x,y2. Which of the following vectors is orthogonal to (3,-1)?O (1,12)O (3,1)O (4,3)O (1,3)

Answered: Image /qna-images/answer/6c2f087a-143d-45e8-8cb0-18a6854ebdef.jpg

Answered: Consider the inner product on R2…

Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following vectors is orthogonal to (3,-1)? O (1,12) O (3,1) O (4,3) O (1,3)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

5. Find the orthogonal projection of the vector b = vectors V₁ = -1- and v2 = onto the subpace E spanned by the (Note that v₁ V₂).
Consider the cross product 'x' of vectors in R3. Is 'x' a binary operation on R3? Is 'x' commutative or associative? Is the dot product of vectors in Rn a binary operation on Rn?
Suppose that ū, ī and w are vectors in a real inner product space such that (7, w) = 16, (T, w) = 5, d(2ū, v) = v27 and ||W|| = V27. Show that 27 - 0 - w = 0.
Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) = = ( Note: Y 2 (x² + y² +2²)³/²¹ (x² + y² + x2)³/²¹ (x² + y² + x2)³/2 • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx = x². Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {Ax, Ay, Az} . Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. • If you need to enter O, enter it in three components, as (0, 0, 0) or {0,0,0}. V x V = ▼ xr= vx= (2A, 2A, 2A₂).
Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”. Fill in the blanks so that the following statements are true. If you believe you don't have enough information to conclude anything for any of the cases, choose the answer "???". Note that there is no intended relationship between the parts. In each case, assume only what the statement says to assume. If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and S C U, then dim(U) 3. If S' is a spanning set for U, then dim(U) 3. If span(S) = U then S If S is a basis for U, then S linearly independent. linearly independent.
(u1 + v1, U2 + v2) and au = (au1, 2), respectively. Let V = {(T,y)r, Y ER}, with addition and scalar multiplication defined as u + v = (u1, U2) and v = (v1, V2) and scalars a. Which of the following is true? where u = O A. k(lu) = (kl)u and 1u = u for all E V O B. (0,0) is the zero of V and (kl)u = k(lu) for all scalars k, l and u E V || O C. Addition is associative and k(u + v) ku + kv for all u, v E V and for all scalars k O D. 3(u + v) : 3u + 3v and the negative of (-2, 3) is (2, –3) O E. k(u + v) = ku + kv for u, v E V and scalar k, and addition is commutative Reset Selection