Select all of the linear transformations from R³ to R³ that are invertible. There may be more than onecorrect answer.A. Trivial transformation (i.e. T(v) = 0 for all v)B. Dilation by a factor of 6C. Rotation about the x-axisD. Identity transformation (i.e. T(v) = v for all v)E. Projection onto the z-axisF. Reflection in the xy-plane

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Answered: Select all of the linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(A) = det(A) from R5x5 to R B. T(A) = trace(A) from R6x6 to R 1 C. T(A) = D. T(A) = AT from R3x5 to R5x3 E. T(A) = A7 from R 4x4 to R4x4 F. T(A) = 6A from R4x5 4x5 to R4 2₁ A from R2x3 to R2x3
Consider the following three transformations from R³ to R³: x1 T x2 x1 - 2x3 2x1 - 2x2 - 5x3 x1 x1+5 x1 S x2 x2 R x2 = 0 X3 -x1 + 2x2+8x3) x3 x1x3 X3 Which of these transformations is/are linear? Select all correct choices. T S R None of these
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Select all of the linear transformations from R³ to R³ that are invertible. There may be more than one correct answer. DA. Rotation about the y-axis B. Projection onto the ay-plane c. Dilation by a factor of 6 D. Reflection in the origin E. Projection onto the z-axis OF. Identity transformation (ue. T() = for all ) 4
38. a. Consider a linear transformation T from R³ to R. What are the possible values of dim(ker T)? Explain. b. Consider a linear transformation T from R4 to R'. What are the possible values of dim(imT)? Explain.
Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be su you can justify your answers. A. T(A) det(A) from R³x³ to R B. T(A) 1A from R4x3 to R4x3 OC. T(A) = AT from R5x3 to R³x5 1 D. T(A) = A 1 from IR to R2x2 6 8 JE. T(A)= A2 from R4x4 to R4x4 6 5 R.T(A)=[74 -97 A from R2x5 to R2x5
For each question below, T: R" → R" where n = 2 or 3 such that T(x) = y. Which of the following transformations are linear? UA. B. C. OD. E. OF. Y1 Y2 Y1 Y2 Y1 Y2 Y1 Y2 Y3 Y1 = = = = Y2 Y1 Y2 = = 0 5x2 7x1 9 2x1 + x2 -X1 -3x1 4x1 6x1 x1 +8 X2 0 X1X2
Q. 3. A transformation T: R² →R² first reflects vectors through the y axis, and then rotates vectors by 3 a. Find the matrix of the transformation T. b. Find the inverse transformation of T , if exists. -1 c. Draw the transformation T for x =| 2
Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(A) = trace(A) from R³x3 to R OB. T(A) AT from R4x5 to R5x4 0 2 C. T(A) = A [²3] A from R2x2 to R²x2 8 6 OD. T(A) A7 from R6x6 E. T(A) = SAS-1 from R2x2 to R2x2, where S = OF. T(A) det (A) from R5x5 to R to R6x6 -7
Use the dot method to add the numbers below. If the number needs a dot, put a dot (period) to the right of the number. Otherwise leave it blank.
Given A = (0,0) and B = (10, 10) and find A' and B'. %3D After finding the new points, show that the following transformations are isometries. Describe whether each is a rotation, reflection, translation/glide, or a combination of 2 transformation. (a) T (x, y) = (-x, y + 2) (b) T (x, y) = (0.6x 0.8y, 0.8x + 0.6y)

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