Question

Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation? Is the...

Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation?

Is the range of T R^3 ? Explain

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the mapping R^3 to R^3 T[x,y,z] = [x-2z, x+y-z, 2y] a) Show that T is...
Consider the mapping R^3 to R^3 T[x,y,z] = [x-2z, x+y-z, 2y] a) Show that T is a linear Transformation b) Find the Kernel of T Note: Step by step please. Much appreciated.
a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3...
a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z) Find the standard matrix for T and decide whether the map T is invertible. If yes then find the inverse transformation, if no, then explain why. b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x...
let let T : R^3 --> R^2 be a linear transformation defined by T ( x,...
let let T : R^3 --> R^2 be a linear transformation defined by T ( x, y , z) = ( x-2y -z , 2x + 4y - 2z) a give an example of two elements in K ev( T ) and show that these sum i also an element of K er( T)
The T: R 4 → R 4 , given by T (x, y, z, w) =...
The T: R 4 → R 4 , given by T (x, y, z, w) = (x + y, y, z, 2z + 1) is a linear transformation? Justify that.
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) = (2y − z, x − z, y + 3x). Use matrices to find the composition S ◦ T. 2. Find an equation of the tangent plane to the graph of x 2 − y 2 − 3z 2 = 5 at (6, 2, 3). 3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find...
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find the Standard Matrix A for the linear transformation b)Find T([1 -2]) c) determine if c = [0 is in the range of the transformation T 2 3] Please explain as much as possible this is a test question that I got no points on. Now studying for the final and trying to understand past test questions.
w ′′ − y + 2z = 3e-x −2w ′ + 2y ′ + z =...
w ′′ − y + 2z = 3e-x −2w ′ + 2y ′ + z = 0 2w ′ − 2y + z ′ + 2z ′′ = 0 w(0) = 1, w′ (0) = 1, y(0) = 2, z(0) = 2, z′ (0) = −2
How many distinct invariant subspaces does the linear operator T: R^3 --> R^3 defined by T(x,y,z)...
How many distinct invariant subspaces does the linear operator T: R^3 --> R^3 defined by T(x,y,z) = (4z-y, x+2z, 3z) have? 0 1 2 3 4
Solve a.      x + y + z = 2, x – y + z = 3, x...
Solve a.      x + y + z = 2, x – y + z = 3, x + y + 2z = 0 b.      5x + y – 2z = 2, x + 2y + 3z = 2, 2x – y = 3
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2...
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2 + z^2 + x^2 <= 1}, and V be the vector field in R3 defined by: V(x, y, z) = (y^2z + 2z^2y)i + (x^3 − 5^z)j + (z^3 + z) k. 1. Find I = (Triple integral) (3z^2 + 1)dxdydz. 2. Calculate double integral V · ndS, where n is pointing outward the border surface of V .