Let W be the set of all vectors of the form shown on the right, where a and brepresent arbitrary real numbers. Find a set S of vectors that spans W, or give anexample or an explanation showing why W is not a vector space.-a +5a-3b5b + aSelect 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+uand (u + v) +w=u+(v +w).O D. The set W is not a vector space because the zero vector is not in W.

The given set, W=-a+5a-3b5b+a|a,b∈ℝ. We have to check whether the set is a vector space or not.

Answered: Let W be the set of all vectors of the…

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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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 +3 a-4b 3b + 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.) 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 the zero vector is not in W. O D. 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).
Determine if v is in the set spanned by the columns of B. B= 8-3 2 -9 4-7 6-2 4 5 -1 10 V= 12 -11 10 11 GETOP Choose the correct answer below and, if necessary, fill in the answer box(es) to complete your choice. OA. Vector v is not in the set spanned by the columns of B because the columns of B, b,, b₂, and b, are linearly independent. B. Vector v is not in the set spanned by the columns of B because the reduced echelon form of the matrix formed by writing B with a fourth column equal to v is OC. Vector v is in the set spanned by the columns of B because the columns of B span R¹. OD. Vector v is in the set spanned by the columns of B because b₁ b₂+ b3 FV. +
Please solve and show all work using Linear Algebra.
Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set S of vectors that spans W or give an example or an explanation to show that W is not a vector space. 4a + 2b 5b + 2c 8c + 8a 7b Select the correct choice and fill in the answer box as needed to complete your choice. O A. A spanning set is S={} (Use a comma to separate answers as needed.) O B. There is no spanning set of W because W does not contain the zero vector. O C. There is no spanning set of W because W is not closed under vector addition. O D. There is no spanning set of W because W is not closed under scalar multiplication.
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 -81 2 V1 = V2 = 18 23 -2 -3 h For what value of h is y in the span of the vectors vị and v2? h =
The vector y is a numerical vector. Which ONE of the following best describes what the R code below will calculate? sum(!is.na(y)) A logical vector of the same length as the vector y, which takes the value TRUE for values in y which are NOT missing and FALSE for values in y which ARE missing. Replaces each value in y with TRUE if it is not missing and FALSE if it is missing The number of non-missing values in the vector y. The number of missing values in the vector y. The propostion of non-missing values in the vector y.
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.

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