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 R3If S is a basis for R3, then write u = (9, 4, 15) as a linear combination of the vectors in S. (Use S1, S2, and s3, respectively, as the vectors in S. If not possible, enterIMPOSSIBLE.)(9,4,15)u=

S to be a basis of . It must contain at least 3 linearly independent vectors in .Clearly we have 3…

Answered: S = {(3, 4, 5), (0, 4, 5), (0, 0, 5)}…

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 =
The set B= {1-ť, - 2t-t, 1+t-t} is a basis for P,. Find the coordinate vector of p(t) = 5- 11t- 11 relative to B. [Plg =O (Simplify your answer.)
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 =
Say you are given two vectors x and y represented using different basis sets {ê;} and {f;}, of the same dimension N. That is, x = y = E y;f;. E xie; and N you are told that a given vector x has the representation x = (1, 1)" in basis {ê;} and the representation x = (-1,1)" in basis {f}}. How might the two basis sets be related? Draw a figure to justify X = your answer.
R is the reduced row echelon form of Q. Find a basis {b₁,b2, ..., bn} for the null space of Q. b₁ = b₂ Fill in vectors in numerical order. Leave blank those that are not needed. = b3 b4 = b5 = 6565 7070 -704 -306 4480 -1573 1694 168 74 - 1073 1579 2314 2492 -248 -108 8138 8764 872 -380 5553 -2613 3317 - 794 1169; R = 4111 -2814 280 122 -1783 - 1320 = 1 0 13 00 1 00 0 0 0 0 0 0 0 2 13 1 0 0 0 8 13 8 0 0 0 10 | 5 13 8 0 0
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=

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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 = (9, 4, 15) as a linear combination of the vectors in S. (Use S₁, S2, and $3, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.)