8.Let the transformation T:R' →R² be given by the formulaT(x,x2,x3) = (2x, – x2, x, +3x;). Find the standard matrix of this transformation andwrite it in matrix multiplication form. Check correctness of your answer for the point(1,4,-3).

Answered: Image /qna-images/answer/72912f16-0cd0-42fc-82c9-3512bfae6951.jpg

Answered: 8. Let the transformation T : R' →R² be…

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 f and g be the linear transformations represented by the matrices (2-1) and (3-3), -5 -4 respectively. What is the image of the point (-1, 1) under the composite transformation go f? O (-4,1) O (-14, 25) O (-12, 6) O(-4,0) O (-15, 24)
Consider the (x, y) vertices of an equilateral triangle in R² given by, (0,0), (1,0), (.5, √3/2) Perform the following actions in order using matrix transformations: (a) Reflect the triangle over the x-axis, (b) Compress the triangle along the y-axis by a factor of 2, (c) Rotate the triangle counterclockwise by π/6 radians about the origin, and (d) Shear the triangle along the x-axis by a factor of 0.5. Clearly show the matrix transformations used and compute the final set of vertices of the triangle.
Find the standard matrix for the linear transformation T(1, 9) — (2а — Зу, т — у, у — 4г) -3 1 -1 1 1 -4 2 1 -4 -3 -1 1 -3 -1 2 1 1 -3 -1 2.
Exercise 273. Show that projw is a linear transformation and that (projw)² = projw.
Find the inverse transformation of y=2x,+x,+x3.y,-x1+x,+2x3,y;=x1-2x3-
Let 4-[1] and W-[*] A = w= -[-1³]. Find k so that there exists a vector X whose image under the linear transformation T(x) = Axis w. Note: The image is what comes out of the transformation. k = Find k so that w is a solution of the equation Ax = 0. k =
Assume that T is a linear transformation and T(1,2,1)=(2,1,3), T(-1,2,3)=(1,1,3), 7(2,1,3)=(1,-1,3), Find the image of (2, 1, 2) under T. Give the components of the answer a₁, a2, a3 as in the ordered triple (a₁, a₂, a3). Using Fractions in simplest form and NO DECIMALS "a₁= "),a2= a3=
4a). The transformation defined by the matrix A = [14 5 stretches images in R² in the directions y = x and y = -x. Figure out the factor by which anything in the y = x direction is stretched and the factor by which anything in the y = -x direction is stretched. 4b). The transformation defined by the matrix B = -82 -55 13 3] stretches images in R2 in one direction by a factor of 3 and some other direction by a factor of 2. Figure out what direction gets stretched by a factor of 3 and what direction gets stretched by a factor of 2. 4c). The transformation defined by the matrix C = stretches images in R2 in two directions. Find the directions and the factors by which it stretches in those directions.
f and g are linear transformations which in matrix form are (0 -4) and (3 3) (2 1) (-5 -4) What is the image of the point (-1,1) under the composite transformation g o f?
Need urgent help please!
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.
Determine whether ?: ?^2 → ?^2, ?(?, ?) = (? + ?, ? − ?) is a linear transformation

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

8. Let the transformation T : R' →R² be given by the formula T(x,x2,x3) = (2x, – x2, x, +3x;). Find the standard matrix of this transformation and | write it in matrix multiplication form. Check correctness of your answer for the point (1,4,-3).