Question

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?

Math   Advanced-Math   
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. 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).
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...
Give augmented matrix for this system. Find all solutions to this system. Indicate all parameters. x1-x2+x3+x4=1...
Give augmented matrix for this system. Find all solutions to this system. Indicate all parameters. x1-x2+x3+x4=1 2x2+3x3+4x4=2 x1-x2+2x3+3x4=3 x1=? x2=? x3=? x4=?
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T ,...
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T , (1,1,1)T ] of R3,, and then find the matrix of the linear transformation T(x1,, x2 , x3 )T = [(4xx+ x2- x3)T , (x1 + 3x3)T , (x2 + 2x3)T with respect to this basis.
Let S = { e1, e2, e3, e4 } be the standard basis for R4 ,...
Let S = { e1, e2, e3, e4 } be the standard basis for R4 , and let B = { v1, v2, v3, v4, } be the basis with vi = T(ei ), where T ( x1, x2, x3, x4 ) = (x2, x3, x4, x1 ). Find the transition matrices P B to S and P S to 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....
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.
7.18) Find the matrix of the cross product transformation Ca: R3-->R3 with respect to the standard...
7.18) Find the matrix of the cross product transformation Ca: R3-->R3 with respect to the standard basis in the following cases: 1) a = e1 2) a = e1 + e2 + e3
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 .
Consider the following system of equations. x1+2x2+2x3 − 2x4+2x5 = 5 −2x1 − 4x3+ x4 −...
Consider the following system of equations. x1+2x2+2x3 − 2x4+2x5 = 5 −2x1 − 4x3+ x4 − 10x5 = −11 x1+2x2 − x3+3x5 = 4 1. Represent the system as an augmented matrix. 2. Reduce the matrix to row reduced echelon form. (This can be accomplished by hand or by MATLAB. No need to post code.) 3. Write the set of solutions as a linear combination of vectors in R5. (This must be accomplished by hand using the rref form found...
3. Consider the system of linear equations 3x1 + x2 + 4x3 − x4 = 7...
3. Consider the system of linear equations 3x1 + x2 + 4x3 − x4 = 7 2x1 − 2x2 − x3 + 2x4 = 1 5x1 + 7x2 + 14x3 − 8x4 = 20 x1 + 3x2 + 2x3 + 4x4 = −4 b) Solve this linear system applying Gaussian forward elimination with partial pivoting and back ward substitution, by hand. In (b) use fractions throughout your calculations. (i think x1 = 1, x2= -1, x3 =1, x4=-1, but i...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT