Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1...
Let D be a 2x2 linear transformation matrix that transforms the vector ? = [ 1 4 ] into the vector ?? = [ 3 6 ] and transforms the vector ? = [ 2 5 ] into the vector ?? = [ 0 9 ]. Analyze the linear transformation matrix D by doing the following: Let S be a square with side length 2, located in the xy-plane. The matrix D transforms the vertices of S into the vertices of another figure P. Find the area of P, and explain the relationship between the determinant of D, the area of S, and the area of P.
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Let D be a 2x2 linear transformation matrix that transforms the
vector ? = [ 1...
linear algebra Remember we were able to express rotations and reflections, which are geometric transformations, using...
linear algebra
Remember we were able to express rotations and reflections, which are geometric transformations, using a linear transformation T, the coef- ficient matrix corresponding to the geometric transformation (r. y) (r', ) (a) What problem do you encounter with translations (r. y) (r+ h.y+k)? To handle this problem, We let the vector (x, y1 ) in R2 correspond to the vector (x1, y1, 1), and conversely. (In effect, we're projecting the :xy-plane onto the plane 1) introduce homogeneous coordinates....
Exercise 5.3.4 Let T be a linear transformation induced by the matrix A = and S...
Exercise 5.3.4 Let T be a linear transformation induced by the matrix A = and S a linear transformation induced by B -al. Find matrix of S oT and find (SoT)(x) for x = 1 2 1 Exercise 5.3.5 Let T be a linear transformation induced by the matrix A = Find the matrix of
(1 point) Consider the transformation T : x = sau - Sov, y = ou +...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
explain your answer please 2. Let T:R3 +R be the linear transformation whose standard matrix is...
explain your answer please
2. Let T:R3 +R be the linear transformation whose standard matrix is 1 2 6 3 7 0 where b is a real number. (a) Compute the determinant of A in terms of b. (b) Find all values of such that the transformation is onto
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A=...
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A= Let T be a linear transformation from IR2 to R2 3 1 ]' Determine the matrix C of the composition ToS
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself,...
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself, we say that is diagonalizable iff there exists a basis S relevant to which can be represented by a diagonal matrix D. Definition 2: If the matrix A represents the linear transformation L with respect to the basis S, then the eigenvalues of L are the eigenvalues of the matrix A. I Definition 3: If the matrix A represents the linear transformation L with...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
please help me with questions 1，2，3 1. Let V be a 2-dimensional vector space with basis...
please help me with questions 1，2，3
1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined o...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix...
linear algebra
Remember we were able to express rotations and reflections, which are geometric transformations, using a linear transformation T, the coef- ficient matrix corresponding to the geometric transformation (r. y) (r', ) (a) What problem do you encounter with translations (r. y) (r+ h.y+k)? To handle this problem, We let the vector (x, y1 ) in R2 correspond to the vector (x1, y1, 1), and conversely. (In effect, we're projecting the :xy-plane onto the plane 1) introduce homogeneous coordinates....
Exercise 5.3.4 Let T be a linear transformation induced by the matrix A = and S a linear transformation induced by B -al. Find matrix of S oT and find (SoT)(x) for x = 1 2 1 Exercise 5.3.5 Let T be a linear transformation induced by the matrix A = Find the matrix of
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
explain your answer please
2. Let T:R3 +R be the linear transformation whose standard matrix is 1 2 6 3 7 0 where b is a real number. (a) Compute the determinant of A in terms of b. (b) Find all values of such that the transformation is onto
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A= Let T be a linear transformation from IR2 to R2 3 1 ]' Determine the matrix C of the composition ToS
Font Styles Paragraph Definition 1: Given La linear transformation from a vector space V into itself, we say that is diagonalizable iff there exists a basis S relevant to which can be represented by a diagonal matrix D. Definition 2: If the matrix A represents the linear transformation L with respect to the basis S, then the eigenvalues of L are the eigenvalues of the matrix A. I Definition 3: If the matrix A represents the linear transformation L with...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
please help me with questions 1，2，3
1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix...
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