T5. Let V = {(a, b, c, d) : a + 3b — 2c = 0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1)¹ form a basisof V.

5) Given that Let, So we have .Hence Noted that .Because Hence basis for subspace V of is

Answered: 5. Let V = {(a, b, c, d): a + 3b-2c=0}.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector of v = (-5,8) with respect to B. 1 2 3 (a) [v]B (b) [v]B (c) [v]B = -3 -3 -2 3 -3 (d) [v]B = (e) [v]B 2
2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a) W is the set of vectors of the form (3s, -2s, s). (b) W is the set of vectors of the form (t – 2, 0,6 – 3t). (c) H is the set of vectors of the form (2b, a, 3b) (d) H is the set of vectors of the form (-b+ 2c, b, 4c),
1. Determine whether the vectors (1,-1) and (1, 1)T are linearly inde- pendent or not. 2. Show that the vectors (1,0,0), (1, 1, 0) and (1,1,1) form a basis of R³. 3. Suppose that the vectors (1, 2, -1,0) and (1,3,2,0) span the sub- space U of R4. Determine whether the vector (1, 1, 1, 0) belongs to U or not.
Find a basis for the plane 4x + 3y + 5z = 0 in R³. |
The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for P₂(R). Let p(t) = 1 + 2t + 4t², find its B-coordinates [p(t)B. =
Let V={(a, b, c, d):a+3b−2c=0}. Show that (−3, 1, 0, 0)T, (2, 0, 1, 0)T, and (0, 0, 0, 1)T form a basis of V.
40. Let H = Span {V1, V2, V3} and B = {V₁, V2, V3}. Show that B is a basis for H and x is in H, and find the B-coordinate vector of x, for -3 -0-0-0-0 , = V3 = 7 -3 = -6 -9 4 -9 5 -8 3 ,X = 4 7 -8 3
a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product
18. Find a basis and dimension of the orthogonal complement to the span ((1, 2, 0, -1), (0, 1, 1, 0), (1, 1, −1, −1)).
: 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

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form a basis of V.