transformation matrix for reflection in line
and the transformation matrixfor areflection in the line y=-x is
.What is the transformation matrix for a reflection in the liney=-5/2x
Homework Answers
transformation matrix for a reflection in the liney=-5x/2
Consider a linear transformation F : R2→R2 In lectures it is shown that the reflection in...
Consider a linear transformation F : R2→R2
In lectures it is shown that the reflection in a subspace can be calcu- lated by Rw(u) = 2 prw(u) – u. Use this formula to find the standard matrix of the linear transformation described above. and hence deter- mine the image of the reflection of the y-axis in the line y = 2x.
For each of the following, find the standard matrix of the given transformation from R2 to...
For each of the following, find the standard matrix of the given transformation from R2 to R2 (a) Counterclockwise rotation through 120 about the origin. sin (a) f дх Ω (b) Projection onto the line y 5 x. sin (a) Ω да (c) Reflection in the line y= x- sin (a) Ω f
in a reflection the image of the line y-2x=3 is the line 2y-x=9
in a reflection the image of the line y-2x=3 is the line 2y-x=9.find the axis of reflection.
(1 point) Match each linear transformation with its matrix. ? 1 10 A. Identity transformation B....
(1 point) Match each linear transformation with its matrix. ? 1 10 A. Identity transformation B. Projection onto the x-axis 0 C. Rotation by 180' Di D. Dilation by a factor of 2 E. Reflection in the y-axis F. Projection onto the y-axis ? 5 s[:] golo [ ] ?
(2) The matrix A-[-5 12 12 5 represents a reflection combined with a scaling by a factor of 13. (a) Find vectors ui and...
(2) The matrix A-[-5 12 12 5 represents a reflection combined with a scaling by a factor of 13. (a) Find vectors ui and v2 such that A is reflection over the line L = span(n) and such that v2 is orthogonal to vi (b) Find the eigenvectors of A with their associated eigenvalues. (c) Find an eigenbasis B for A (a basis of R2 consisting of eigenvectors of A). (d) what is the matrix of the linear transformation T(z)...
For each of the following, find the standard matrix of the given transformation from R2 to...
For each of the following, find the standard matrix of the given transformation from R2 to R2. (a) Clockwise rotation through 30° about the origin. a ab sin(a) 22 ar (b) Projection onto the line y = -42. a ab sin(a) !!! 22 8 (c) Reflection in the line y = 1 a ab sin(a) 22 ? Әr
A 2 x 2 matrix A is associated with the transformation that reflects vectors in the plane across ...
A 2 x 2 matrix A is associated with the transformation that reflects vectors in the plane across the line y = 2x. Sketch the vector field (use your discretion and draw vectors until you believe that you have captured the big picture) corresponding to A. In other words, for every ~w, we place A ~w at the head of ~w.
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in...
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in the y-axis E. Rotation through an angle of 90° in the counterclockwise direction -1 0 0.5 0 0 0.5 0 -1 F. Reflection in the r-axis 0 -1
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
(3 pts) 7. The following matrix represents a reflection onto a line in RP: 4/5 -3/5]...
(3 pts) 7. The following matrix represents a reflection onto a line in RP: 4/5 -3/5] (-3/5 -4/5 Find the equation of the line.
Consider a linear transformation F : R2→R2
In lectures it is shown that the reflection in a subspace can be calcu- lated by Rw(u) = 2 prw(u) – u. Use this formula to find the standard matrix of the linear transformation described above. and hence deter- mine the image of the reflection of the y-axis in the line y = 2x.
For each of the following, find the standard matrix of the given transformation from R2 to R2 (a) Counterclockwise rotation through 120 about the origin. sin (a) f дх Ω (b) Projection onto the line y 5 x. sin (a) Ω да (c) Reflection in the line y= x- sin (a) Ω f
(1 point) Match each linear transformation with its matrix. ? 1 10 A. Identity transformation B. Projection onto the x-axis 0 C. Rotation by 180' Di D. Dilation by a factor of 2 E. Reflection in the y-axis F. Projection onto the y-axis ? 5 s[:] golo [ ] ?
(2) The matrix A-[-5 12 12 5 represents a reflection combined with a scaling by a factor of 13. (a) Find vectors ui and v2 such that A is reflection over the line L = span(n) and such that v2 is orthogonal to vi (b) Find the eigenvectors of A with their associated eigenvalues. (c) Find an eigenbasis B for A (a basis of R2 consisting of eigenvectors of A). (d) what is the matrix of the linear transformation T(z)...
For each of the following, find the standard matrix of the given transformation from R2 to R2. (a) Clockwise rotation through 30° about the origin. a ab sin(a) 22 ar (b) Projection onto the line y = -42. a ab sin(a) !!! 22 8 (c) Reflection in the line y = 1 a ab sin(a) 22 ? Әr
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in the y-axis E. Rotation through an angle of 90° in the counterclockwise direction -1 0 0.5 0 0 0.5 0 -1 F. Reflection in the r-axis 0 -1
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
(3 pts) 7. The following matrix represents a reflection onto a line in RP: 4/5 -3/5] (-3/5 -4/5 Find the equation of the line.
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