o (translation in R2) Determine whether the function is a linear transformation. T: R2 + R2,...
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
linear algebra Determine whether the function is a linear transformation. T: R2 R3, T(x, y) = (x,xy, vy) O linear transformation O not a linear transformation
Determine whether the function is a linear transformation. T: R2 R3, T(x,y) = (Vx, 5xy, vy) O linear transformation not a linear transformation
Determine whether or not the following transformation T :V + W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T, (iii) determine if T is one-to-one, (iv) determine if T is onto. : (a) T: R3 + R2 defined by T(x, y, z) = (2x, y, z) (b) T: R2 + R2...
By justifying your answer, determine whether the function T is a linear transformation. (a) T : R3 → M2,2 defined as x+y T(x, y, z) = x – 3z x - y (b) T : P2 → R defined as T (a + bx + cx?) = a – 2b + 3c. +
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 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
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
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)