Question

Problem 2. Show that T is a linear transformation by finding a matrix that implements the...

Problem 2. Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors.

(a) T(x1, x2, x3, x4) = (0, x1 + x2, x2 + x3, x3 + x4)

(b) T(x1, x2, x3, x4) = 2x1 + 3x3 − 4x4 (T : R4 → R)​

Please show T is a linear transformation for part (a) and (b).

Math   Algebra   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that...
Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) = (0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 − 4x4 (T : R 4 → R) Problem 3. (20 pts.) Which of the following statements are true about the transformation matrix...
Find the standard matrix for the following transformation T : R 4 → R 3 :...
Find the standard matrix for the following transformation T : R 4 → R 3 : T(x1, x2, x3, x4) = (x1 − x2 + x3 − 3x4, x1 − x2 + 2x3 + 4x4, 2x1 − 2x2 + x3 + 5x4) (a) Compute T(~e1), T(~e2), T(~e3), and T(~e4). (b) Find an equation in vector form for the set of vectors ~x ∈ R 4 such that T(~x) = (−1, −4, 1). (c) What is the range of T?
Determine if the linear transformation is (a) one-to-one, (b) onto. T(x1,x2,x3)=(2x1 −4x2,x1 −x3,−x2 +3x3).
Determine if the linear transformation is (a) one-to-one, (b) onto. T(x1,x2,x3)=(2x1 −4x2,x1 −x3,−x2 +3x3).
2X1-X2+X3+7X4=0 -1X1-2X2-3X3-11X4=0 -1X1+4X2+3X3+7X4=0 a. Find the reduced row - echelon form of the coefficient matrix b....
2X1-X2+X3+7X4=0 -1X1-2X2-3X3-11X4=0 -1X1+4X2+3X3+7X4=0 a. Find the reduced row - echelon form of the coefficient matrix b. State the solutions for variables X1,X2,X3,X4 (including parameters s and t) c. Find two solution vectors u and v such that the solution space is \ a set of all linear combinations of the form su + tv.
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T...
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an orthogonal matrix ?I any case,find the eigen values and eigen vectors of A .
Solve the linear systems that abides by the following rules. Show all steps. I. The first...
Solve the linear systems that abides by the following rules. Show all steps. I. The first nonzero coefficient in each equation is one. II. If an unknown is the first unknown with a nonzero coefficient in some equation, then that unknown doesn't appear in other equations. II. The first unknown to appear in any equation has a larger subscript than the first unknown in any preceding equation. a. x1 + 2x2 - 3x3 + x4 = 1. -x1 - x2...
in parts a and b use gaussian elimination to solve the systems of linear equations. show...
in parts a and b use gaussian elimination to solve the systems of linear equations. show all steps. a. x1 - 4x2 - x3 + x4 = 3 3x1 - 12 x2 - 3x4 = 12 2x1 - 8x2 + 4x3 - 10x4 = 12 b. x1 + x2 + x3 - x4 = 2 2x1 + 2x2 - 2x3 = 3 2x1 + 2x2 - x4 = 2
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T...
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T (x) = Ax that reflects a vector (x1, x2) about the x2-axis. (b) Find a linear transformation S : R2 → R2 such that T(x) = Bx that rotates a vector (x1, x2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the...
Find eigenvectors associated with the eigenvalues of the following linear operator: (please show all steps) V=...
Find eigenvectors associated with the eigenvalues of the following linear operator: (please show all steps) V= R^3; T(x1,x2,x3) = (x1+x2, 2x2+2x3, 3x3)
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system...
x1-5x2+x3+3x4=1 2x1-x2-3x3-x4=3 -3x1-3x3+7x3+5x4=k 1 ) There is exactly one real number k for which the system has at least one solution; determine this k and describe all solutions to the resulting system. 2 ) Do the solutions you found in the previous part form a linear subspace of R4? 3 ) Recall that a least squares solution to the system of equations Ax = b is a vector x minimizing the length |Ax=b| suppose that {x1,x2,x3,x4} = {2,1,1,1} is a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT