MTH501 Assignment 2 Solution Fall 2021

MTH501 Assignment 2 Solution Fall 2021

In today’s we will cover MTH501 assignment 2 solution

Before Going to assignment Solution we will discuss its topic

So here are the Topics of our Assignment

Diagonalization

Diagonalization is a process of transforming a vector A to the form A = PDP for some invertible matrix P and a diagonal matrix D. In this lecture, the factorization enables us to compute A k quickly for large values of k which is a fundamental idea in several applications of linear algebra. Later, the factorization will be used to analyze (and decouple) dynamical systems.

The “D” in the factorization stands for diagonal. Powers of such a D are trivial to compute.

Example 3 is same as Question No 1

Null Spaces, Column Spaces, and Linear Transformations

Subspaces arise in as set of all solutions to a system of homogenous linear equations as the set of all linear combinations of certain specified vectors. In this lecture, we compare and contrast these two descriptions of subspaces, allowing us to practice using the concept of a subspace. In applications of linear algebra, subspaces of Rusually arise in one of two ways:

·  as the set of all solutions to a system of homogeneous linear equations or

·  As the set of all linear combinations of certain specified vectors.

Our work here will provide us with a deeper understanding of the relationships between the solutions of a linear system of equations and properties of its coefficient matrix.