Question

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

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
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.
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?
Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find...
Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find the diagonal matrix A' for T relative to the basis B'. A = −1 −2 0 −1 0 0 0 0 1 , B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)}
In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3...
In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3 (that is, ej has a 1 in the jth position, and has 0 everywhere else). (a) Suppose that D is a 3 × 3 diagonal matrix. Show that e1, e2, e3 are eigenvectors of D. (b) Suppose that A is a 3 × 3 matrix, and that e1, e2, and e3 are eigenvectors of A. Is it true that A must be a diagonal...
b) More generally, find the matrix of the linear transformation T : R3 → R3 which...
b) More generally, find the matrix of the linear transformation T : R3 → R3 which is u1  orthogonal projection onto the line spanu2. Find the matrix of T. Prove that u3 T ◦ T = T and prove that T is not invertible.
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T:...
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T: R2 -> R3 first rotate point through (pie)/2 radian (counterclock-wise) and then reflects points through the horizontal x-axis b) Use part a to find the image of point (1,1) under the transformation T Please explain as much as possible. This was a past test question that I got no points on. I'm study for the final and am trying to understand past test questions.
Determine whether or not the transformation T is linear. If the transformation is linear, find the...
Determine whether or not the transformation T is linear. If the transformation is linear, find the associated representation matrix (with respect to the standard basis). (a) T ( x , y ) = ( y , x + 2 ) (b) T ( x , y ) = ( x + y , 0 )
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.
1. List the algebraic properties of the cross product in R3. On the same line, write...
1. List the algebraic properties of the cross product in R3. On the same line, write the algebraic property of the dot product in R3 if it exists. example (a) cross-product_________dot product if the same property. 2. Demonstrate how to find the area of a parallelogram when given u = -6i + -4j + k and v = 3i + 5j + 9k
Find the standard matrix for the linear transformation f(a, b, c, d)=(b-c+d, 2b-3d). Find the standard...
Find the standard matrix for the linear transformation f(a, b, c, d)=(b-c+d, 2b-3d). Find the standard matrix for the linear transformation that flips the xy plane over the y axis and rotates it by π/4 radians CCW.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT