If possible, write down an example of a matrix with the following properties. If it is not possible to do so, write not possible. You do not need to justify your reasoning.
Homework Answers
Reflection about the line 
is given by
Projection onto the 
axis is given by
Composing the two matrices, we obtain our desired matrix
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If possible, write down an example of a matrix with the
following properties. If it is...
Do you want to restart to instal updates now or try tonight? Problem 1. For each of the following linear transformation...
Do you want to restart to instal updates now or try tonight? Problem 1. For each of the following linear transformations, draw two linearly independent eigenvectors (i.e., one eigen- vector should not be a scalar multiple of the other). Mark the angle between your vector and the nearest axis or dashed line (when the angle is nonzero). Example) The transformation which mirrors vectors over the line making a 20° angle with the horizontal axis 200 200 a) The transformation which...
Determine if there exists a linear transformation T: R2 -> R2 with the following properties. If...
Determine if there exists a linear transformation T: R2 -> R2
with the following properties.
If yes, give an example. If no, explain why such a
transformation is not possible.
(4) Determine if there exists a linear transformation T: R2 + R2 with the following properties. If yes, give an example. If no, explain why such a transformation is not possible. (a) T is one-to-one and onto. (b) T is not one-to-one. (c) T is not onto. (d) T is...
8. Find the standard matrix representation for each linear operator L: R2 + R2 described below:...
8. Find the standard matrix representation for each linear operator L: R2 + R2 described below: (a) L rotates each vector 7 by 45° in the clockwise direction. (b) L reflects each vector 7 about the 21 axis and then rotates it 90° in the counterclockwise direction. (c) L doubles the length of t and then rotates it 30° in the counterclockwise direction. (d) L reflects each vector 7 about the line x2 = 21 and projects it onto the...
need in 10 mins qno 12 A is identity matrix escite eeometrically the effeet of the transformation T 12) Let A-o Defi...
need in 10 mins
qno 12 A is identity matrix
escite eeometrically the effeet of the transformation T 12) Let A-o Define a transformation T by T(x)-Ax. Find the standard mnatrix of the linear transformation T. 13) T: 2-R2 first performs a vertical shear that maps e1 into e1 +2e2, but leaves the vector e2 unchanged, then reflects the result through the horizontal x1-axis.
escite eeometrically the effeet of the transformation T 12) Let A-o Define a transformation T by...
[E] Consider the linear transformation T: R3 → R3 given by: T(X1, X2, X3) = (x1...
[E] Consider the linear transformation T: R3 → R3 given by: T(X1, X2, X3) = (x1 + 2xz, 3x1 + x2 + 4x3, 5x1 + x2 + 8x3) (E.1) Write down the standard matrix for the transformation; i.e. [T]. (E.2) Obtain bases for the kernel of T and for the range of T. (E.3) Fill in the blanks below with the appropriate number. The rank of T = The nullity of T = (E.4) Is T invertible? Justify your response....
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2....
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
I need help with the last part of this question (ie: Write the standard matrix for...
I need help with the last part of this question (ie: Write the
standard matrix for H∘T, where H is the reflection of R2 about the
line y=x.)
Consider the linear transformation T: R4_R2 defined as T(11,12,13,14)=(-211 +12 +214,-312-14). Find the standard matrix for T: sina) a dr f -2 1 0 2 -3 0-1 2 What is the dimension of ker(T)? Is T one-to-one? NO Enter one: yes no Write the standard matrix for HoT where H is the...
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so...
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so that (a) T is one-to-one (b) T is not one-to-one but onto (c) T is neither one-to-one nor onto
Consider the linear transformation T: R3 + R2 defined as T(X1, X2, 23)=(-23, -3 &1 –...
Consider the linear transformation T: R3 + R2 defined as T(X1, X2, 23)=(-23, -3 &1 – 23). Write the standard matrix for HoT, where H is the reflection of R2 about the y-axis. ab sin (a) a дх f a 12 ?
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax...
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
Do you want to restart to instal updates now or try tonight? Problem 1. For each of the following linear transformations, draw two linearly independent eigenvectors (i.e., one eigen- vector should not be a scalar multiple of the other). Mark the angle between your vector and the nearest axis or dashed line (when the angle is nonzero). Example) The transformation which mirrors vectors over the line making a 20° angle with the horizontal axis 200 200 a) The transformation which...
Determine if there exists a linear transformation T: R2 -> R2
with the following properties.
If yes, give an example. If no, explain why such a
transformation is not possible.
(4) Determine if there exists a linear transformation T: R2 + R2 with the following properties. If yes, give an example. If no, explain why such a transformation is not possible. (a) T is one-to-one and onto. (b) T is not one-to-one. (c) T is not onto. (d) T is...
8. Find the standard matrix representation for each linear operator L: R2 + R2 described below: (a) L rotates each vector 7 by 45° in the clockwise direction. (b) L reflects each vector 7 about the 21 axis and then rotates it 90° in the counterclockwise direction. (c) L doubles the length of t and then rotates it 30° in the counterclockwise direction. (d) L reflects each vector 7 about the line x2 = 21 and projects it onto the...
need in 10 mins
qno 12 A is identity matrix
escite eeometrically the effeet of the transformation T 12) Let A-o Define a transformation T by T(x)-Ax. Find the standard mnatrix of the linear transformation T. 13) T: 2-R2 first performs a vertical shear that maps e1 into e1 +2e2, but leaves the vector e2 unchanged, then reflects the result through the horizontal x1-axis.
escite eeometrically the effeet of the transformation T 12) Let A-o Define a transformation T by...
[E] Consider the linear transformation T: R3 → R3 given by: T(X1, X2, X3) = (x1 + 2xz, 3x1 + x2 + 4x3, 5x1 + x2 + 8x3) (E.1) Write down the standard matrix for the transformation; i.e. [T]. (E.2) Obtain bases for the kernel of T and for the range of T. (E.3) Fill in the blanks below with the appropriate number. The rank of T = The nullity of T = (E.4) Is T invertible? Justify your response....
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
I need help with the last part of this question (ie: Write the
standard matrix for H∘T, where H is the reflection of R2 about the
line y=x.)
Consider the linear transformation T: R4_R2 defined as T(11,12,13,14)=(-211 +12 +214,-312-14). Find the standard matrix for T: sina) a dr f -2 1 0 2 -3 0-1 2 What is the dimension of ker(T)? Is T one-to-one? NO Enter one: yes no Write the standard matrix for HoT where H is the...
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so that (a) T is one-to-one (b) T is not one-to-one but onto (c) T is neither one-to-one nor onto
Consider the linear transformation T: R3 + R2 defined as T(X1, X2, 23)=(-23, -3 &1 – 23). Write the standard matrix for HoT, where H is the reflection of R2 about the y-axis. ab sin (a) a дх f a 12 ?
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
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