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How was the linear transformation of b1 and b2 were applied (L(b1) , L(b2))? NOTE: b1=(1,1)^T , b2=(-1,1)^T Linear Transformations EXAMPLE 4 Let L be a linear transformation mapping R? into itself an...
How was the linear transformation of b1 and b2 were applied
(L(b1) , L(b2))?
NOTE: b1=(1,1)^T , b2=(-1,1)^T
Linear Transformations EXAMPLE 4 Let L be a linear transformation mapping R? into itself and defined by where (bi, b2] is the ordered basis defined in Example 3. Find the matrix A represent- ing L with respect to [bi, b2l Solution Thus, A0 2 onofosmation D defined by D(n n' maps P into P, Given the ordered
Linear Transformations EXAMPLE 4 Let...
14. Fix a non-zero vector n R". Lot L : Rn → Rn be the linear mapping defined by L()-2 proj(T), f...
PART C ONLY! Thank you.
14. Fix a non-zero vector n R". Lot L : Rn → Rn be the linear mapping defined by L()-2 proj(T), fa TER or all (a) Show that if R", Such that oandj-n -0, then is an eigenvector of L What is its cigenvaluc? (b) Show that is an cigenvector of L. What is its cigenvalue? (c) What are the algebraic and geometric multiplicities of all cigenvalues of L?
14. Fix a non-zero vector n...
Consider the linear transformation T : R2 + R2 defined as T(21,12)=(0,21 – 12). Find the...
Consider the linear transformation T : R2 + R2 defined as T(21,12)=(0,21 – 12). Find the standard matrix for T: a ab sin(a) 8 f E д 0 0 1 What is the dimension of ker(T)? Is T one-to-one? no 47 Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the z-axis. a ab sin(a) f 12 II 8 R ат
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where...
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
R2 defined as Consider the linear transformation T: R2 T(21,22)=(0,21 – 22) Find the standard matrix...
R2 defined as Consider the linear transformation T: R2 T(21,22)=(0,21 – 22) Find the standard matrix for T: a ab sin (a) f 8 ат What is the dimensi of ker(T)? Is T one-to-one? Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the 3-axis. a sin(a) f 22 8 R a E är (Alt + A)
h-." 72 16, Let T : R2 → M2×2 be the mapping defined by T (...
h-." 72 16, Let T : R2 → M2×2 be the mapping defined by T ( :' Show that T is a linear transformation.
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x,...
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
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...
Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 –...
Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 – 22). I (a) In the standard basis for R2 and R, what is the matrix A that corresponds to the linear transformation L? (5 points) (b) Let U = {(1,1), (-1,2)}. Find the transition matrix from U to the star dard basis for R. (5 points) (c) Let V = {(1,0), (-1,1)). Find the transition matrix from the standard basis for R2 to V....
How was the linear transformation of b1 and b2 were applied
(L(b1) , L(b2))?
NOTE: b1=(1,1)^T , b2=(-1,1)^T
Linear Transformations EXAMPLE 4 Let L be a linear transformation mapping R? into itself and defined by where (bi, b2] is the ordered basis defined in Example 3. Find the matrix A represent- ing L with respect to [bi, b2l Solution Thus, A0 2 onofosmation D defined by D(n n' maps P into P, Given the ordered
Linear Transformations EXAMPLE 4 Let...
PART C ONLY! Thank you.
14. Fix a non-zero vector n R". Lot L : Rn → Rn be the linear mapping defined by L()-2 proj(T), fa TER or all (a) Show that if R", Such that oandj-n -0, then is an eigenvector of L What is its cigenvaluc? (b) Show that is an cigenvector of L. What is its cigenvalue? (c) What are the algebraic and geometric multiplicities of all cigenvalues of L?
14. Fix a non-zero vector n...
Consider the linear transformation T : R2 + R2 defined as T(21,12)=(0,21 – 12). Find the standard matrix for T: a ab sin(a) 8 f E д 0 0 1 What is the dimension of ker(T)? Is T one-to-one? no 47 Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the z-axis. a ab sin(a) f 12 II 8 R ат
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
R2 defined as Consider the linear transformation T: R2 T(21,22)=(0,21 – 22) Find the standard matrix for T: a ab sin (a) f 8 ат What is the dimensi of ker(T)? Is T one-to-one? Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the 3-axis. a sin(a) f 22 8 R a E är (Alt + A)
h-." 72 16, Let T : R2 → M2×2 be the mapping defined by T ( :' Show that T is a linear transformation.
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
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...
Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 – 22). I (a) In the standard basis for R2 and R, what is the matrix A that corresponds to the linear transformation L? (5 points) (b) Let U = {(1,1), (-1,2)}. Find the transition matrix from U to the star dard basis for R. (5 points) (c) Let V = {(1,0), (-1,1)). Find the transition matrix from the standard basis for R2 to V....
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