Linear transformations/matrix Theory

The composition of any two reflections, whose lines of reflection are orthogonal, is a half-turn. See attached file for full problem description.

Linear Algebra/linear transformation Problem

Given the plane: x-y in 3 space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigen values for this matrix d) compute the eigen vectors for these eigen values

Linear algebra

Given the plane(x, -y, 0) This is the plane that is parallel with the Z axis and intersects the x,y plane through the line x-y=0 in 3 space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigen values for this matrix d) compute the eigen vectors for these eigen values

Linear Operations

Need to figure out how to do this type of problem. Using A =[ Cos alpha - Sin alpha ] Sin alpha Cos alpha (1) Find A^-1 =[ ] E SO sub 2 (1R) (2) Check A inverse is in SO sub2 (R) Check A inverse * A = Identity and A * A inverse = Identity SHow that SO sub 2 ( R) is abelian .

Linear algebra and taylor series

Taylor series of e^A. See attached file for full problem description.