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Problem: Find the matrix which represents in standard coordinates the transformation S:R2R2 which...
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2...
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2 which shear parallel to the line L ai , where a (3,6) such that a gets transformed into a s, with s (-18,9) Solution The approach we take demonstrates how much convenience can be gained by being able to work with respect to coordinates which are specially adapted to the situation at hand. We compute the matrix S in two steps 1. We find...
Give the standard matrix for the transformation which sends Give the standard matrix for the transformation...
Give the standard matrix for the transformation which sends Give the standard matrix for the transformation which sends (- () and sends ( 1 ) -(9) sends
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix w...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L:...
15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L: R3 R2 defined by L u2 4u U3 Find the standard matrix representing L. U1 0 b) L:R2 R3 defined by z ([,]) Find the standard matrix representing L. c) Find L(() using the standard matrix and linear transformation in part b. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the...
136. Transformations for Different Bases. Find the matrix A that represents the linear transformation T with...
136. Transformations for Different Bases. Find the matrix A that represents the linear transformation T with respect to the bases B and B'. (a) T:R3M2,2 given by T(4, 0, 2) =: -20 where B = {e1,e2, C3} and B' = {EM i = 1, 2; j = 1,2} (i.e. the standard basis for M2,2). (b) T:P3 + P3 given by T(ao + ax + a2r? + agr) = (do + a2) - (ai +203) where B, B' = {1,2,2, "}.
(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...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
You may use a calculator and/or computer to carry out calculations. However you must show a...
You may use a calculator and/or computer to carry out calculations. However you must show a sufficient amount of work to clearly communicate your solution to the reader. [A] Consider the L-shaped polygon with vertices: (-1,0), (1,0), (1,1), (0,1), (0,3), and (-1,3) shown to the right. Find the standard matrix for each of the transformations described below. Then use matrix multiplication to obtain the coordinates for the 6 vertices that result from applying the transformation to the vertices of the...
Please solve correctly (10) 7. Below is the transformation matrix between cylindrical and rectangular coordinates: e...
Please solve correctly
(10) 7. Below is the transformation matrix between cylindrical and rectangular coordinates: e coso singoi = -sin cos0 . 2 0 0 1 k When we found the velocity and acceleration in cylindrical coordinates, we had to find how each of the unit vectors changed in time. For this problem, just find For this problem, just find as g and di and dt dt
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2 which shear parallel to the line L ai , where a (3,6) such that a gets transformed into a s, with s (-18,9) Solution The approach we take demonstrates how much convenience can be gained by being able to work with respect to coordinates which are specially adapted to the situation at hand. We compute the matrix S in two steps 1. We find...
Give the standard matrix for the transformation which sends Give the standard matrix for the transformation which sends (- () and sends ( 1 ) -(9) sends
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L: R3 R2 defined by L u2 4u U3 Find the standard matrix representing L. U1 0 b) L:R2 R3 defined by z ([,]) Find the standard matrix representing L. c) Find L(() using the standard matrix and linear transformation in part b. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the...
136. Transformations for Different Bases. Find the matrix A that represents the linear transformation T with respect to the bases B and B'. (a) T:R3M2,2 given by T(4, 0, 2) =: -20 where B = {e1,e2, C3} and B' = {EM i = 1, 2; j = 1,2} (i.e. the standard basis for M2,2). (b) T:P3 + P3 given by T(ao + ax + a2r? + agr) = (do + a2) - (ai +203) where B, B' = {1,2,2, "}.
(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...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
You may use a calculator and/or computer to carry out calculations. However you must show a sufficient amount of work to clearly communicate your solution to the reader. [A] Consider the L-shaped polygon with vertices: (-1,0), (1,0), (1,1), (0,1), (0,3), and (-1,3) shown to the right. Find the standard matrix for each of the transformations described below. Then use matrix multiplication to obtain the coordinates for the 6 vertices that result from applying the transformation to the vertices of the...
Please solve correctly
(10) 7. Below is the transformation matrix between cylindrical and rectangular coordinates: e coso singoi = -sin cos0 . 2 0 0 1 k When we found the velocity and acceleration in cylindrical coordinates, we had to find how each of the unit vectors changed in time. For this problem, just find For this problem, just find as g and di and dt dt
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