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1. ### Calc III freshman year

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...
2. ### Linear algebra multiple choice

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...
3. ### Linear algebra - rank

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?
4. ### Linear algebra - basis multiple choice questions

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...
5. ### Linear Algebra - vector spaces

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...