Let 3 be the setDetermine if B is a basis for R³ and check the correct answer(s) below.A. B is not a basis because it does not span R³.B. B is a basis.C. B is not a basis because it is not a linearly independent set.-26--CIGD35=

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Answered: Let 3 be the set Determine if 3 is a…

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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10. In R3, let S be the set of vectors -1 1 S = {v1,V2, V3, V4} = 4 -3 -2 %3D -4 0. -4 Explain why S spans R³ but is not a basis for R3. Delete one of the vectors from S to form a new set of vectors, that is a basis for R3. a. b.
Find all possible real numbers a, b, c, d ER such that form a basis B= (v, w) for R2 that satisfies -(:)--() and w= [CL-G) Warning: Do not forget to check that your possible choices of a, b, c, d ensure that v and w are in fact a basis for R². I understand that I need to submit my solution in Assign2.
03. Write the standard basis for the vector space 1. R 2. R4 4. MA 3. Мад 5. P 6. P, 04. Determine whether S is a basis for the indicated vector space. 1. S ((3.-2), (4, 5)) for R 2. S ((1,5, 3), (0, 1, 2), (0, 0, 6)} for R 3. S (0, 3.-2). (4, 0. 3). (-8. 15. - 16)} for R' 4. S {(-1, 2.0, 0). (2.0.-1,0). (3, 0, 0. 4), (0, 0, 5, 0)} for R 5. S (-21+ 1.r-4.+2r, 5t) for P. 6. S (4-4.1 6r.r+3r, 4r- 1) for Py
Pick every true statement which applies to the following set of vectors. {8·4)} O This set spans R^3 O Every vector in its span can be written uniquely as a linear combination of these vectors O This set of vectors is linearly dependent O This set is a basis of R^3 O None of the above answers are true
1) Let W: = 3a +10b+ 7c+32d 2a + 8b+ 6c +24d -5a + (-13) b + (-8) c + (-46) d] la + 2b + 1c + 8d la + 3b + 2c + 10d Then a basis for W would be: a b - 2) Let W = C : -6a-6b-5c+ d = 0 and 9a+10b+9c+ (-2) d + e = 0. d e Then a basis for W would be:
Consider the following. {{::}[ :}| 1 0 0 1 1. 1 V = M,2, B = 0 1 -1 1 1 -1 Complete the following statements. The elements of set B ---Select-- v linearly independent. The set B has elements and dim(M22) Therefore, the set B ---Select- v a basis for v. Need Help? Read It
Let A = 0 -2 0 2 -3 -2 2 1 -4 2 -2 1 6 4 -3 -2 4 -2 2 a. A basis for the column space of A is { }. You should be able to explain and justify your answer. Enter a coordinate vector, such as or , or a comma separated list of coordinate vectors, such as , or ,. b. The dimension of the column space of A is answer): A. rref(A) has a pivot in every row. B. The basis we found for the column space of A has three vectors. OC. Three of the five columns in rref(A) have pivots. OD. Two of the five columns in rref(A) have pivots. □ E. rref(A) has a pivot in every column. □ F. rref(A) is the identity matrix. c. The column space of A is a subspace of d. The geometry of the column space of A is the origin inside R^5 because (select all correct answers -- there may be more than one correct because each column vector in A is a vector in R^4
Determine if the set of vectors shown to the right is a basis for R³. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R³. Which of the following describe the set? Select all that apply. A. The set spans R³. B. The set is a basis for R³. C. The set is linearly independent. D. None of the above 3 2 -3 2 - 12
3= b, ,b2} and C= (c,.c2} be bases for a vector space V, and suppose b, = - 6c, + 5c2 and b2 = - 4c, +2c2. a. Find the change-of-coordinates matrix from B to C. b. Find (x]c for x = - 5b, + 3b2. Use part (a). a. P = C-B b. (xlc (Simplify your answers.)
--|-- If vi = , v2 = |0|v3 , then {v1, v2, v3} is for R. 2 3 Select one: A. a basis B. None of thses answers C. not a basis

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Let 3 be the set Determine if 3 is a basis for R³ and check the correct answer(s) below. A. 3 is not a basis because it does not span R³. B. 3 is a basis. C. B is not a basis because it is not a linearly independent set. 6 --COD B = 3 0