Let T be a linear transformation from R to P2 defined by-(E)T=(-2a1 + a2 + 4a3)x² + (a1 – 7a2)x + 8a2 – 5aza3Let Bbe a basis for R3 and B' = {x², x, 1}be a basis for P2a11a12a13Find the standard matrix A of T with respect to B and B' . If A =а21а22a23thenаз1а32a33a11 =, а12a13a21 =a22 =, a23аз1a32 =a33 =

Answered: Image /qna-images/answer/1e515e06-4006-4ef9-bd59-3884eebfb3f9.jpg

Answered: Let T be a linear transformation from…

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

If the matrix of change of basis form the basis B to the basis B' is A = (³) O A. OB. 04 (3) 00 (12) 52 21 then the first column of the matrix of change of basis from B to B is:
Let T and T2 two linear transformations from R? to R², defined by 7(;) - ) ()-() 3x - 2y (;) (} x+ y T1 T2 y - 3x for all (x, y)" e R?. Find the standard matrix representations for each of the following composite functions, and their inverse transformation, if they exist, by using the algorithm for matrix inversion in Lemma 3, Topic 14. )T followed by T2. (i) T2 followed by an anticlockwise rotation by angle 5 in R?. (ii) A reflection in the line y = 2x followed by a projection onto the line y = -3x in R2.
Let T be a linear operator defined on P3 by T(a0+a1x+a2x^2)=a0+a1(x-1)+a2(x-1)^2. The third row of the matrix associated with T with respect to base 1, x, x^2 is: a) (0,0,1) b) other response c) (1,-2,1) d) (1,0,0) e) (-1,1,0)
5. Find the orthogonal projection of b = (1,-1,2) onto the left null space of the matrix A = -6
a) Verify the given sequence B is a basis ; and b) compute the images of the standard basis vectors with respect to the given linear transformation. 15. fi = 1+2x – 2x2, f2 = 2 + 3x – 4x2, f3 = 1 + 4x – x², B = (f1, f2, f3). - 1 T(fi) = (; 10)- 4 T(fi) = (; ).T ,T(f2) : 3 8
8-3) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2,... are not vectors but are entries in vectors a) T(x1, x2) = (2x2-3x1, x1-4x2, 0, x2) b) T(x1, x2, x3, x4) = 2x1 + 3x - 4x4 (T:R* → R)
9. Consider the following 2 x 2 matrix A and basis S of R²: A ¹ = [² %) and 5 = {[_¹₂] · [_³;]} The matrix A defines a linear operator on R². Find a matrix B that represents the mapping A relative to the basis S.
7-8. Determine whether the space of the matrix A 2- I 2 O > Am 4 vector ū belongs A₁ = 0 to null
33. Prove that the row vectors of an n x n invertible matrix A form a basis for Rn.
1. Let u₁, U2, U3 } and { V₁, V2, V3 } be ordered bases for R³, where H and U₁ = 2 1 U₂ = 1 V1 = 1 -1 -2 U3 = -8-0-0 V2 = 1 V3 (a) Determine the transition matrix corresponding to a change of basis from the ordered basis {u₁, U2,, u3} to the ordered basis {V₁, V2, V3}. (b) Write vector z = 2u₁ - 3u₂ + u3 as Use this transition matrix to find the coordinates of with respect to {V₁, V2, V3}.
of Let W be the set of all 2 × 2 matrices [a b] C d basis for W is S = (a) • X (b) following questions: • Y = • r {[ || (c) where, c = 0 and d = 2a - 3b. A || •S= 1 x ] []} " S О У I dim(W) - Answer the
21. Suppose that A {a1,a2} is a basis of the vector space V = R? and B, = a1 + 2a2, B2 = 201 + 5a2. (a) Prove that B = {B,,B,} is also a basis of V. %3D (b) Find the following coordinate matrices : [B1]A, [B,]B, [a1]a and [a2]B. (c) Find the transition matrix (=Change of basis matrix) from A to B

SEE MORE QUESTIONS

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