5.Let T: R³ R2 be the transformation defined byT (:) -(3x - 2y + 4z5x - 9z+4²)Is T is a linear transformation? If it is, prove it and find its standard matrix. If it isnot, give a counterexample.

Answered: Image /qna-images/answer/66276e0d-e442-4431-bbd4-e83fe5eb0b7d.jpg

Answered: 5. Let T: R³ R2 be the transformation…

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

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.
-9 V₁ = --[-] and X₂ such that T(x) is Ax for each x. Let x = A = X₁ -2 [3] and let T: R² R² be a linear transformation that maps x into x₁v₁ +X₂V₂. Find a matrix A -8 and V₂ =
Find the matrix of the linear transformation T from R? R?, where T([1, 0]) = [1, -2], and T([2, 1]) = [2, 3] (Note: matrix A = [T([1,0]), T([0, 1])] ). 1 (a) 1 (b) 1. (c) -2 1 -2 3 -2 1 (d) 0. 3
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.
Let = A = = 6 3 by T(x) = x x. || a1 S az X b₁ b₂ b3 = | a2bვ — a3b2 a3b₁-a₁b3 La₁b₂-a₂b₁ Find the matrix A of the linear transformation from R³ to R³ given
Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and, interpreting T as a matrix, det(T) # 0. Let P be the parallelogram which is the image of the square D = = [0, 1] × [0, 1] (i.e. T(D) =P). Then the area of P is given by O lad - bcl ad bc abcd 1 |ad - bc| O labcd|
Let T: R2→R2 be a linear transformation with standard matrix X2 A-[2, a, az . where a, and a, are the vectors shown in the - 1 figure. Using the figure, draw the image of under the 3 transformation T. Choose the correct graph below. O A. ОВ. Oc. OD. X2 X2 X2 T(-1,3) T(-1,3) a2 a2 a2 a2 a1 a1 a1 T(-1,3) T(-1,3)
Assume that T is a linear transformation. Find the standard matrix of T. T: R2→R2 first reflects points through the vertical x2-axis and then reflects points through the line X2 =X1. A =
assume that T is a linear transformation. Find a Standard matrix of T. T: IR² →IR" 8) where A T(e₁) = (5,1,5,1) T(e₂) = (-3₁7,0,0) ? e₁ = (1,0) € 2 = (0₁1) (integer or decimal)

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 T: R³ R2 be the transformation defined by T (:) - = (3x - 2y + 4z 5x - 9z +42) Is T is a linear transformation? If it is, prove it and find its standard matrix. If it is not, give a counterexample.