COMPUTER-BASED: HOMEWORK SET #1

EE 510: Linear Algebra for Engineering

Directions: Please include all necessary plots and carefully explain your reasoning.

1. Let random vector X be a 2D-Gaussian vector with mean and covariance matrix Kxx-

We have

-[X].

where ₁ and 2 are the respective means of X₁ and X₂, ₁² and 2² are the respective

variances of X₁ and X₂, and 12 is the covariance between X₁ and X₂. Note that 012021

so Kxx is a symmetric matrix (Kxx Kxx").

Let X be a Gaussian vector such that:

-B₁

b) Define the ellipsoid E₂ where

-4).

Ex=

f) Repeat 1(a)-1(d) with

Kxx =

Ex=

a) Randomly select 5,000 samples from the 2D-Gaussian distribution with mean Ex and

covariance Kxx and plot the samples. (You can use the code provided in Figure 1

below or any other software).

- B.

Kxx =

- 89.

Assigned: 11 October 2023

Due: 21 October 2023

&₂ = {x= [7₁₁7₂] : (x−µx)¹K¹(x − £x), ₁ R, 1₂ €R}.

c) Derive the principal axes of E₂. Find their respective lengths.

d) Sketch the ellipsoid &2. Compare this plot with the sample plot.

e) Repeat 1(a)-1(d) with

- 8.

012

021 0₂²

Kxx=

Kxx =

(1)/n