4. Decide which of the following sets of vectors are subspaces of R2. Justify your answers.a₁such that a₁ > α₂.a) The set S₂ consisting of all vectorsa2b) The set S3 consisting of all vectorsc) The set S4 consisting of all vectorsd) The set S₁ consisting of all vectorsa₁a2[a]a1a2such that a₁ a₂ = 0.such that a₁ a₂ ≥ 0.] such that a² + a² := 0.

Answered: Image /qna-images/answer/40a0da2d-f3fe-4d58-97f5-218f1867a8ac.jpg

Answered: 4. Decide which of the following sets…

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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A) The set of all polynomials of the form ax³ bx² - cx + 2, where a,b and car real numbers is a subspace of P3 Select one: O True O False
Suppose that v = (v1, v2, ..., vn) and û = (u₁, U2, ..., Un) are a pair of n-dimensional vectors. Assume that each component of the vector is a real number, so 7 and u are both members of the set R¹. We will say that and u are "almost the same" when every component of is close to every component of ū. That is, v₁ is close to u₁, v2 is close to u2, etc (practically speaking, "close" means that their absolute difference is small). Assume that we are given the predefined predicate CloseTo(x, y) and the integer constant n. Use them to write a formal definition of the new predicate Almost The Same (7, u) which asserts that n dimensional vector is almost the same as ū. Tip: It is not legal to say i v to refer to a component of v, because is not a set. Instead, use vi to refer to the ith component of v. What set would i belong to in this case?
The question is in the attached picture
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, S2, and S3, respectively, for the vectors in the set.) S = {(1, 2, 3, 4), (1, 0, 1, 2), (3, 8, 11, 14)} (0, 0, 0, 0) = Express the vector s3 in the set as a linear combination of the vectors s and sɔ. S3 =
1. Determine if these vectors are linearly independent or linearly dependent. If they are linearly independent show this. If they are linearly dependent, write a nontrivial linear combination (at least some coefficients need to be nonzero) of them being equal to 0. {4.0-6)}
Consider vectors C = 5ar− 3a + 2a and D = 3a, – 2a0 – 4a in spherical coordinates. (a) Transform C and D to rectangular coordinates if they are located at (5,30°,60°). (b) obtain the addition, subtraction, dot product and cross product of C and D in spherical coordinates and rectangular coordinates.
а +с] a) Let S Find three vectors in R3 so that each vector a - b - a in S can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 -2 1 1 1 -1 Let A = 2 Determine whether the rows of A are 4 4 -5 [-2 -4 4 -1 linearly independent. Evaluate | – 2A²| and13A¬1|.
3
1- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (-3,0,4), (5,-1,2), (1,1,3) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 2- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthonormal basis for R³, then obtain an orthonormal basis from them. Express (3,7,-4) as a linear combination of the orthonormal basis. 3- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (1,1,0), (0,0,1), (0,1,1) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 4- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthogonal basis for R³, then obtain an orthonormal basis from them. Express (2,3,-4) as a linear combination of the orthonormal basis. 5- Find the coordinates of the vector u = (0,25, 1) with respect to the orthogonal basis v₁ = ( 3,4,0), V₂ = (−4, 3, 0 ) and v₂ = (−4,3,0) 6- Find the coordinates of the vector U = (7,5,2) with respect to the basis V₁ =…
Plz solve both

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