a. Find a nonzero element X in W.XLet V be the vector space of symmetric 2 x 2 matrices and W be the subspaceW = span{b. Find an element Y in V that is not in W.Y2[²-2-2-3-2 25|}.

Let be the vector space of symmetric matrices and be the subspace.a. Find a nonzero element in…

Answered: a. Find a nonzero element X in W. X Let…

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 B be the standard basis of the space P₂ of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. - 5t+t², 1+5t-t²2, 2+t+t², +8t-3t² G Does the set of polynomials span P₂? O A. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P2. O B. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R³. By isomorphism between R³ and P2, the set of polynomials does not span P2. OC. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R². By isomorphism between R² and P2, the set of polynomials does not span P2. ⒸD. Yes; since the…
The null space for the matrix is spanned by the vector 0 5 2 4 -1 1 0 1 1 2 -1 6 4 5 4
Determine whether (V₁, V₂, V3] is a basis for R³. H. V2 V₁ = No OYes = 8 8 N V3 -2 [-7]
Let 4 be a linear combination of {u₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} = span{u₁, U2₂, U3, 14} when u4 is a scalar multiple of one of {U₁, U₂, U3}. B. span{u₁, U₂, U3} = span{U₁, U₂, U3, U4}. c. We only know that span{u₁, U₂, U3} span{u₁, U₂, U3, U4} . D. There is no obvious relationship between span{u₁, U₂, U3} and span{u₁, U₂, U3, U4} . E. none of the above
Find a basis of the subspace of R5 spanned by the following vectors: 4 1 -1 8 6 6 -2 2 12 16 -1 -2 2 -2 2 5 3 -2 10 4 5 3 -2 10 4

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a. Find a nonzero element X in W. X Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace b. Find an element Y in V that is not in W. Y -2 -2 - span([23] [23]). |}. -2 -3 5 W = "