Show that the transformation T defined by T(x₁, x₂) = (2x₁ - 4x₂, x₁ +5, 6x₂) is not linear.If T is a linear transformation, then T(0) = and T(cu + dv) = cT(u) +dT(v) for all vectors u, v in the domain of T andall scalars c, d.(Type a column vector.)

Answered: Image /qna-images/answer/10b557e0-fd7d-4cd7-b947-abe06d16d4e1.jpg

Answered: Show that the transformation T defined…

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

Let denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: 03 → be the function that sends a polynomial to its derivative. That is, D(p(x)) = p'(x) for all polynomials p(x) E 3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + a₁x + aº and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in 3 and c E R. a. D(p(x) + q(x)) = D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = ? choose b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) E 3? choose c. Is D a linear transformation? choose . (Enter a3 as a3, etc.)
(a) Let u and v be (fixed, but unknown) vectors in R". Suppose that T: R" → R" is a linear transformation such that T(u) = 6u + v and T(v) = 4u - 2v. Compute (T. T)(v), where TT is the composition of T with itself. Express your answer as a linear combination of u and v. (ToT)(v) = 10 u + -1 V Incorrect answer. Incorrect answer. (b) Let v and w be (fixed, but unknown) vectors in R", which are not scalar multiples of each others. Suppose that T: R" → R" is a linear transformation such that T(4v+3w) = -2v-2w and T(v+1w) = 5v+2w. Compute T(v) and express it as a linear combination of v and w. T(v) = 4 v + 2 W Incorrect answer. Incorrect answer.
5. Consider a linear transformation T: R2 → R2 which reflects a vector about the line y=-x, and dilates the reflected vector by a factor of 2. Find the standard matrix for the linear transformation.
Suppose M is a linear transformation taking vectors in R² to vectors in R2, where M(1,0)=(2,-4) M(0, 1) = (-6,6) M(2,9) = (
Suppose T is a linear transformation, where (1, 0, 0) T(u) T(7) (0, 1,0) W (0,0,1) T(w) Then I can be represented by the matrix ū V = = = T= = = = (5, -3, -2) (-2,-1,0) (0,5, 4)
2. Let T : R² → R² be a linear transformation such that: 1 -2 (i) T maps vector u = into the vector a = [ 5 3 (ii) T maps vector v = [³] into the vector b = [ Use the fact that T is a linear transformation to find T(3u +2v). -4
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)
Let e1= (1,0) e2=(0,1), x1=(1,6) and x2=(4,−5) Let T: R2→R2 be a linear transformation that sends e1→x1 to and e2→x2. If T maps (−5,−8) to the vector y→, then y = ___

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

Show that the transformation T defined by T(x₁, x₂) = (2x₁ - 4x₂, x₁ +5, 6x₂) is not linear. If T is a linear transformation, then T(0) = and T(cu + dv) = cT(u) +dT(v) for all vectors u, v in the domain of T and all scalars c, d. (Type a column vector.)