11–14 A region R in the
R is the parallelogram with vertices
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- A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.arrow_forwardSketch the image of the unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation.T is the expansion represented by T(x, y) = (5x, y).arrow_forwardA. Plot the circles x2+y2=4 and x2+y2=1 on the same coordinate plane. B. Find the image of any point on x2+y2=4 under the transformation (x,y)→(12x,12y). The point (2,0) will go to the ordered pair ( , ) C. What do you notice about x2+y2=4 and x2+y2=1 ? The small circle is a of the larger one using the origin as a center and a scale factor ofarrow_forward
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- Let S = {z: 1 =< Re(z) =< 2 & 1 =< Im(z)}. Find the image of transformed region w-plane under bi-linear transformation of f (z) = (z + 1)/(z – 1). (Hint: Note that a semi-line, a line segment or a circular arc can be transformed to a semi-line, line segment or a circular arc under bi- linear transformation. A line is specified completely, if two point on line is determined, while a circle is specified completely if three distinct points are determined.)arrow_forwardApply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.arrow_forward1 Find a Householder transformation P such that P [2, 1,1]T= k[1, 0, 0]T. Find the valueof the constant..arrow_forward
- Select all of the linear transformations from R³ to R³ that are invertible. There may be more than one correct answer A. Rotation about the z-axis B. Trivial transformation (.e. T(v) = 0 for all C. Projection onto the yz-plane D. Dilation by a factor of 8 E. Identity transformation (Le T(v) = v for all ) F. Reflection in the originarrow_forwardIsosceles trapezoid RSTU, with K as midpoint of RS, Las midpoint of ST , M as midpoint of TU , and N as midpoint of RU , is shown. Point P is the intersection of KM and NL. RK S P M Which transformation carries the trapezoid onto itself? O A. a 90* rotation clockwise about P O B. a 180° rotation clockwise about P O c. a reflection over KM D. a reflection over NLarrow_forward3. Let T:R2→R2 be the linear transformation that first rotates points clockwise through 150∘ (5π/6 radians) and then reflects points through the line y=x. Find the standard matrix A for T. 4. Find the characteristic polynomial of the matrixarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning