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2. Consider a reflection in the y-axis, dilation factor of In(2), rotation through, and a contraction...
(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...
Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x,...
Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= (b) Use A to find the image of the vector v. T(V) =
(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 [ ] ?
#3. Let L:R → Ro be the transformation defined by 1-211 - 312 3:12 - 203...
#3. Let L:R → Ro be the transformation defined by 1-211 - 312 3:12 - 203 22-23 Find the 3 x 2 matrix representation of L. #4. Find if the lincar transformation L is the composition of the following liscar transforma- tions: a contraction, with a dilation factor - followed by rotation in counter clockwise direction for an angle = (n=90), followed by a reflection around the Iy axis, followed by rotation in clockwise direction for an angle a
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.
Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find...
Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find the standard matrix A for the linear transformation T. A- It (b) Use A to find the image of the vector v T(V) (c) Sketch the graph of vand its image. 3 T(v) 2 2 1 -3 2 - - 2 -1 2 1 3 -1 -1 -2 T(v) -31 -3 O T (v) 3 2 2 11 1
(4) (a) Determine the standard matrix A for the rotation r of R 3 around the z-axis through the a...
(4) (a) Determine the standard matrix A for the rotation r of R
3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and find the image of the point C) under the transformation. a. A transformation which moves points to one quarter of their original distance to the origin. b. A transformation which first rotates points counterclockwise through an angle 31/2, then reflects them across the y-axis. A transformation which first reflects points across the y-axis, then rotates them counterclockwise through an angle 31/2.
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the stand...
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the standard matrix of T1? (b) Suppose T : R2R is the counterclockwise rotation by 8 J. What is A2, the standard matrix of T2? (c) What is the image of (2,-4) under T- Ti o T2?
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z....
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y),...
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= 1 (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of v and its image. у 6 у 6 V 5: 5 41 4 3 3 T(v) 2 2 11 1 X 1 -6 -5 -4 -3 -2 -1 -A 2...
(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...
Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= (b) Use A to find the image of the vector v. T(V) =
(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 [ ] ?
#3. Let L:R → Ro be the transformation defined by 1-211 - 312 3:12 - 203 22-23 Find the 3 x 2 matrix representation of L. #4. Find if the lincar transformation L is the composition of the following liscar transforma- tions: a contraction, with a dilation factor - followed by rotation in counter clockwise direction for an angle = (n=90), followed by a reflection around the Iy axis, followed by rotation in clockwise direction for an angle a
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.
Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find the standard matrix A for the linear transformation T. A- It (b) Use A to find the image of the vector v T(V) (c) Sketch the graph of vand its image. 3 T(v) 2 2 1 -3 2 - - 2 -1 2 1 3 -1 -1 -2 T(v) -31 -3 O T (v) 3 2 2 11 1
(4) (a) Determine the standard matrix A for the rotation r of R
3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and find the image of the point C) under the transformation. a. A transformation which moves points to one quarter of their original distance to the origin. b. A transformation which first rotates points counterclockwise through an angle 31/2, then reflects them across the y-axis. A transformation which first reflects points across the y-axis, then rotates them counterclockwise through an angle 31/2.
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the standard matrix of T1? (b) Suppose T : R2R is the counterclockwise rotation by 8 J. What is A2, the standard matrix of T2? (c) What is the image of (2,-4) under T- Ti o T2?
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z....
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= 1 (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of v and its image. у 6 у 6 V 5: 5 41 4 3 3 T(v) 2 2 11 1 X 1 -6 -5 -4 -3 -2 -1 -A 2...
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