Consider the following "standard" basis of R³ over R:--000=Let q be the real quadratic form (from R³ to R) defined via:q(x1, x2, x3) = 9x² + 7x² + 2x3 + 18x1x2 + 18x1x3 + 10x2x3Determine [q], the symmetric matrix representing the quadratic form q in terms of the basis &:

Answered: Image /qna-images/answer/d6b8eea3-d266-4c15-8191-5f130f190eb1.jpg

Answered: Consider the following "standard" basis…

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

In P,, find the change-of-coordinates matrix from the basis B = {1 + 5t, - 6+t- 29t,1 - 6t} to the standard basis. Then write t as a linear combination of the polynomials in B. find the change-of-coordinates matrix from the basis B to the standard basis. In P2: 1 - 6 1 1 - 6 C-B 5 - 29 (Simplify your answer.) Write t as a linear combination of the polynomials in B. ? =(1+5?) +(-6+t-291) +1 – 6t) %3D (Simplify your answers.)
Solve all parts or will dislike
The set B = {2 + 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x) = 84 − 39x + 80x² relative to this basis: - [p(x)]B=
Determine whether the following vectors form a basis of R4: 2 4 8 -2 4 -8
Let 1 -4 A = - -2 2 6 -3 2 10 Find an orthonormal basis of the column space of A.
In P2, find the change-of-coordinates C = {1,t,t²}. Then find the B-coordinate vector for −4+7t-4t². matrix from the basis B = {1 - 2t+t²,3-5t + 4t²,1 + 4t²} to the standard basis
Consider the basis B = {({2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for an arbitrary pair (c, d) EV, the set {x1(c, d), x2(c,d)) is equal to: {(3d-c), (c-2d)} {(3d+ c), (c+ 2d)} {(2d-c), (c + 3d)} {(2d+c), (c + 3d)} {(3d+c), (2c - d)}
The set B = {-(2 + 2x²), - (6+4x+6x²), 18 + 8x + 16x²} is a basis for P₂. Find the coordinates of p(x) = - (32 + 8x +26x²) relative to this basis: [p(x)] B =
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…
Q16 Please provide justified answer asap to get a upvote
The set B = {− (3 + 4x²), − (6 + 3x + 8x²), 8 + 6x + 8x²} is a basis for P₂. Find the coordinates of p(x) - [p(x)]B = (56 +30x + 64x²) relative to this basis:
Consider the basis B = {({2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for an arbitrary pair (c, d) EV, the set {x1(c, d), x2(c,d)) is equal to: {(3d-c), (c-2d)} {(3d+ c), (c+ 2d)} {(2d-c), (c + 3d)} {(2d+c), (c + 3d)} {(3d+c), (2c - d)}

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

Consider the following "standard" basis of R³ over R: --000 = Let q be the real quadratic form (from R³ to R) defined via: q(x1, x2, x3) = 9x} + 7x² + 2x3 + 18x1x2 + 18x1x3 + 10x2x3 Determine [q], the symmetric matrix representing the quadratic form q in terms of the basis &: