Let A for some real numbers a and b, i. Show that the vector is an Eigen vector of the matrix A. ii. Find the Eigen values of the matrix A. ii. Find the Eigen vectors corresponding to each Eigen values found in part (b). iv. Diagonalize the matrix A, using the Eigen vectors found in part (b), that is find the matrix P such that (P-1 A P) is a diagonolize matrix.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.