Determine whether S is a basis for R³.S = {(3, 5, 4), (0, 5, 4), (0, 0, 4))S is a basis for R³.S is not a basis for R3.If S is a basis for R³, then write u = (9, 10, 16) as a linear combination of the vectors in S. (Use S₁, S₂, and s3, respectively, as the vectors in S. If not possible, entIMPOSSIBLE.)251-52 +353 xU=

The given set of vectors .We have to find the vectors form a basis of and find a linear combination…

Answered: Determine whether S is a basis for R³.…

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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Determine whether S is a basis for R³. S = {(3, 4, 5), (0, 4, 5), (0, 0, 5)} OS is a basis for R³. OS is not a basis for R³. If S is a basis for R³, then write u = (6, 4, 20) as a linear combination of the vectors in S. (Use S₁, S₂, and s3, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.) U= Need Help? X Read It Watch It
Determine whether S is a basis for R. S = {(3, 5, 4), (0, 5, 4), (0, 0, 4)} O S is a basis for R3. O S is not a basis for R3. If S is a basis for R, then write u = (6, 5, 12) as a linear combination of the vectors in S. (Use s1, s2, and s3, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.) u =
Determine whether S is a basis for R3. S = {(3, 2, 5), (0, 2, 5), (0, 0, 5)} O s is a basis for R3. O s is not a basis for R3. If S is a basis for R3, then write u = (9, 2, 15) as a linear combination of the vectors in S. (Use s1, 52, and s3, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.) u =
Find the representation of (-5, 5, 1) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (-5, 5, 1) in terms of the ordered basis B = {ï,j,k}. [(-5, 5, 1)]B= b. Represent the vector (-5,5, 1) in terms of the ordered basis C = (ē3, ē1, ë2). [(-5, 5, 1)]c = c. Represent the vector (-5, 5, 1) in terms of the ordered basis D = {-2, -ē1, ē3}. [(-5, 5, 1)]D=
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D

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