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(1 point) Match each linear transformation with its matrix. ? 1 10 A. Identity transformation B....
(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...
4AHW8: Problem 18 Previous Problem Problem List Next Problem (1 point) To every linear transformation T...
4AHW8: Problem 18 Previous Problem Problem List Next Problem (1 point) To every linear transformation T from R2 to R2, there is an associated 2 x 2 matrix. Match the following linear transformations with their associated matrix. 1. Counter-clockwise rotation by 1/2 radians 2. Reflection about the y-axis 3. Reflection about the line y=X 4. Clockwise rotation by 1/2 radians 5. Reflection about the x-axis 6. The projection onto the x-axis given by T(x,y)=(x,0) 1 0 A. B. 1 0...
Find L (4 3 ) if the linear transformation L is the composition of the following...
Find L (4 3 ) if the linear transformation L is the composition
of the following linear transformations: a dilation, with a
dilation factor c = 3, followed by rotation in counterclockwise
direction for an angle α = π, (α = 180 ), followed by a reflection
around the x1–axis.
#1. Find 2(())) if the linear #4. Find L if the linear transformation L is the composition of the following linear transforma- tions: a dilation, with a dilation factor c=3,...
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
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
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation...
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the follo...
1,5
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the following: (a) stretch by a factor of c (sketch the original vector and the resulting vector) (b) rotation by an angle of ф (sketch the original vector, the angle of rotation, 716 Appendix B. Selected Topics from Linear Algebra and the resulting vector) original vector, the line of projection, and the resulting vector) the original vector, the line of reflection, and the...
#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
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Problem 13. Let l be the line in R' spanned by the vector u = 3...
Problem 13. Let l be the line in R' spanned by the vector u = 3 and let P:R -R be the projection onto line l. We have seen that projection onto a line is a linear transformation (also see page 218 example 3.59). a). Find the standard matrix representation of P by finding the images of the standard basis vectors e, e, and e, under the transformation P. b). Find the standard matrix representation of P by the second...
(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...
4AHW8: Problem 18 Previous Problem Problem List Next Problem (1 point) To every linear transformation T from R2 to R2, there is an associated 2 x 2 matrix. Match the following linear transformations with their associated matrix. 1. Counter-clockwise rotation by 1/2 radians 2. Reflection about the y-axis 3. Reflection about the line y=X 4. Clockwise rotation by 1/2 radians 5. Reflection about the x-axis 6. The projection onto the x-axis given by T(x,y)=(x,0) 1 0 A. B. 1 0...
Find L (4 3 ) if the linear transformation L is the composition
of the following linear transformations: a dilation, with a
dilation factor c = 3, followed by rotation in counterclockwise
direction for an angle α = π, (α = 180 ), followed by a reflection
around the x1–axis.
#1. Find 2(())) if the linear #4. Find L if the linear transformation L is the composition of the following linear transforma- tions: a dilation, with a dilation factor c=3,...
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
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
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
1,5
In Problems 1-9, consider the given vector x. Find the vectors that result from each of the following: (a) stretch by a factor of c (sketch the original vector and the resulting vector) (b) rotation by an angle of ф (sketch the original vector, the angle of rotation, 716 Appendix B. Selected Topics from Linear Algebra and the resulting vector) original vector, the line of projection, and the resulting vector) the original vector, the line of reflection, and the...
#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
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Problem 13. Let l be the line in R' spanned by the vector u = 3 and let P:R -R be the projection onto line l. We have seen that projection onto a line is a linear transformation (also see page 218 example 3.59). a). Find the standard matrix representation of P by finding the images of the standard basis vectors e, e, and e, under the transformation P. b). Find the standard matrix representation of P by the second...
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