50. (Recommended)Suppose all vectors x in the unit square 0 ≤ x₁ ≤ 1,0 ≤ x₂ ≤ 1 aretransformed to Ax (A is 2 by 2).(a) What is the shape of the transformed region (all Ax)?(b) For which matrices A is that region a square?(c) For which A is it a line?(d) For which A is the new area still 1?

Answered: Image /qna-images/answer/a1d5d51b-f466-4f12-9eec-429e3a9935c0.jpg

Answered: 50. (Recommended) Suppose all vectors x…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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?
(a) 1 (b) 2 (c) 0 (d) 3 (e) all the above 4 1 a, 8 15. If the matrix 4 D -1 then the column space of is vectors a, e R , such that (a) a, +2a, = 0 (b) a, +a, = ((c) a,-2a) = 0 aand b (e) b and c
Find the decomposition a = a|| + a₁ with respect to b if a = (3, 4, 2), b = (3, 4, 6). = (a||x, a||y, a||z) a¹b = (alx, aly, alz) (Enter the components of vectors using symbolic notation and fractions where needed.) a||x ally a||z ab = = = alx = aly = alz =
Suppose we have three vectors x, y. and z all of which are the same length. We wish to perform a least squares fit where we can write z = ao + a1x + a2Y what do have to minimise? Select one: ao a. Iz- a2 O b. lz - | 2 Y a2 || 1 ao O c lz -| a1 O d. You cannot compute this. నా
C. Ture or False . . . D. Ture or False . . .
5. Let P be the square with corners (0,0), (1,-1), (1,1), and (2,0). Compute ffpy-x dA.
3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4
6. ceC(4) 7. Givep that D- then N(D) contains B All vectors that belong to both N(A) nd N(B) 6. All vectors that belang to N(A) All vectors that belong to N(A+ B) 4 All vectors that belong to N(AB) N(B)
Needed to be solved correctly in 10 minutes in the order to get positive feedback please show me neat and clean work for it by hand solution needed
If Q =I- auu" where Qis an orthogonal matrix, a > 0, and u E Rx real vector, and I is n x n identity matrix then O a lu|| -1 O b. u|| - /2 O c u - O d. lu|| - 0.5 O O
令ll. 1:0€ 团 / IMG_20210210_170723.jpg HWO Use Gramer Rule to Find K,2 -2x + 3y-Z = 1 X + 23-2-4 -2x -j +2 = -3 How@D Find the area of A ABC Where Hhe are AL1,-1,2), B(2,1,-1) and vectors cl-1,1, 2).

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