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...
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...
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...