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 linearlyindependent 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.C-232

Answered: Image /qna-images/answer/0b30339d-ecf2-4ccf-8d56-a86de6613f74.jpg

Answered: Determine if the set of vectors shown…

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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H H Select all of the vectors that are in the span of {u₁, u₂}. (Check every statement that is correct.) Let u₁ = A. The vector 9 B. The vector D. The vector and u₂ [] OC. All vectors in R² are in the span. E. The vector F. The vector 8 -5 -5 is in the span. -51 is in the span. is in the span. is in the span. +9 [-] is in the span. G. We cannot tell which vectors are in the span.
Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans W, or give an example or an explanation showing why W is not a vector space. -a +5 a-3b 5b + a Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The set W is a vector space and a spanning set is S= (Use a comma to separate vectors as needed.) O B. The set W is not a vector space because not all vectors u in W have the property 1u= u. O C. The set W is not a vector space because not all vectors u, v, and w in W have the property that u + v=v+u and (u + v) +w=u+(v +w). O D. The set W is not a vector space because the zero vector is not in W.
Let U₁ = 5 -1 3 and u₂ = Select all of the vectors that are not in the span of {u₁, U₂}. 10 A. The vector 7-3 5 10 -3 5 5 +3–1 3 OG. The vector is not in the span. 10 -3 is not in the span. OB. The vector 5 OC. All vectors in R3 are in the span. OD. The vector 1 is not in the span. 0 10 ☐ E. The vector 3-3 is not in the span. 5 [0 OF. The vector 0 is not in the span. 0 6+5+4] 6 *-1 is not in the span. 6 * 3 5 OH. The vector -1 is not in the span. 3 7 * 10 1. The vector 7*-3 +3 5 H -1 is not in the span. 3 7*5 + [1 OJ. The vector 0 is not in the span. 0 OK. We cannot tell which vectors are in the span.
Consider the following vectors: 3 9. 6 -2 -5 -6 a = 8 1 1 9. For each of the following vectors, determine whether it is in span{a, 6. c}. If so, express it as a linear combination using a, b, and c as the names of the vectors above. 9. V1 = 9. -7 -15 13 -8 -17 18 -10 16
Set B 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the vertices of a parallelogram. 2. Let Ā and B be nonzero vectors. Find k eR such that Ā - kB is orthogonal to Ā + B.
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
Let u4 be a linear combination of {u₁, U2, U3}. Select the best statement. ● A. {u₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above
Express the indicated vector w as a linear combination of the given vectors v₁ and v₂ if this is possible. If not, show that it is impossible. W = -7 - 9 - 2 3 5 8 -4 - 3 Select the correct answer below, and fill in the answer box(es) to complete your choice. ) v₁ + ( ) v₂. A. It is possible to express the vector w in terms of v₁ and v₂, as w= (Type integers or fractions.) B. It is impossible to express the vector w in terms of V₁ and V₂, because an echelon form of the augmented matrix [V₁ V₂ W], E= (Type an integer or simplified fraction for each matrix element.) shows that the system is inconsistent.
Express the indicated vector w as a linear combination of the given vectors v1 and v2 if this is possible. If not, show that it is impossible. w= (-1,0,7), V1= (7,6,5), v2=(6,5,3) Select the correct answer below, and fill in the answerbox(es) to complete your choice. A.It is possible to express the vector w in terms of v1 and v2, as w=(___)v1+(___)v2. (Type integers or fractions.) B.It is impossible to express the vector w in terms of v1 and v2, because an echelon form of the augmented matrix [v1 v2 w], E=___?, shows that the system is inconsistent.

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