Recent content by underacheiver

hey guys, i need some advice as to which math class to enroll in. i just got accepted to college and will be starting first semester of freshman year in september. i will be a math major, and i am really comfortable with math. So right now, i am in ap calc BC and i am confident that i can get...

Homework Statement 1. If A is a real symmetric matrix, then there is a diagonal matrix D and an orthogonal matrix P so that D = P T AP. a. True b. False 2. Given that λi and λj are distinct eigenvalues of the real symmetric matrix A and that v1 and v2 are the respective eigenvectors associates...

i finally got b for 4 and e for 5 for 4, b completes the theorum in one of my textbooks. for 5, i solved the nullity of Dx as 0, thus the rank has to be 3? is that correct?

so is it 3? because the 2nd and 4th columns are dependent.

The column rank of a matrix A is the maximal number of linearly independent columns of A. Likewise, the row rank is the maximal number of linearly independent rows of A. Since the column rank and the row rank are always equal, they are simply called the rank of A.

How do you figure out the right answer?? 4. if it doesn;t span U then does it span V? 5. is the answer b? because i don't see how it can be anything else then.

ah~ ok, i see. thank you.

Homework Statement Find the rank of A = {[1 0 2 0] [4 0 3 0] [5 0 -1 0] [2 -3 1 1]} Homework Equations The Attempt at a Solution i row reduced A to be: {[1 0 0 0] [0 1 0 -1/3] [0 0 1 0]} where do i go from here?

Homework Statement 1. Which of the following is not a linear transformation from 3 to 3? a. T(x, y, z) = (x, 2y, 3x - y) b. T(x, y, z) = (x - y, 0, y - z) c. T(x, y, z) = (0, 0, 0) d. T(x, y, z) = (1, x, z) e. T(x, y, z) = (2x, 2y, 5z) 2. Which of the following...

but t(1,1,1) can be written as a linear combination of the set {(1,0,0),(0,1,0),(0,0,1)}. am i getting something mixed up here?

For part c, why is the nullity 1? The kernel is (t,t,t) so its basis is {(1,0,0),(0,1,0),(0,0,1)} is that not 3 dimensions?

Homework Statement part a. Use the matrix A = {[1,-1,0] [0,-1,1] [-1,2,-1]} to compute T(x) for x = {[1] [2] [3]} Here, T:R^3-->R^3 is defined as T(x)=Ax. part b. describe the kernel of the transformation. part c. what is the nullity of the tarnsformation part d. what...