[SOLVED] COEN140 Lab #2-Linear Algebra

Note: matrix and vector operations can be found in lecture slides COEN140_02_LinearAlgebraReview.pdf.

1. Create a 2×5 matrix 𝐀 with elements as random float numbers from 0 to 1. Print the rank of 𝐀.

Let 𝐁 = 𝐀𝐀^𝑇, find the shape and rank of 𝐁

Let 𝐂 = 𝐀^𝑇𝐀, find the shape and rank of 𝐂

2. Create a 3×5 matrix 𝐗 with elements as random integers from 0 to 10, and find the dimension (shape) of 𝐀 = 𝐗𝐗^𝑇 by coding;

Create a 3×1 column vector 𝐰 with elements as random integers from 0 to 10, and find the dimension of 𝐀𝐰 by coding;

Find the dimension of 𝐰^𝑇𝐀 by coding;

Find the dimension of 𝐰^𝑇𝐀𝐰 by coding.

Find a way (by coding) to verify that 𝐗𝐗^𝑇 is symmetric.

Calculate 𝐀⁻¹. Print 𝐀⁻¹𝐀 and 𝐀𝐀⁻¹.

3. Create a 5×1 column vector 𝐱 with elements as random float numbers from 0 to 1. Calculate 𝐱𝐱^𝑇 by coding. What do you think is the rank of 𝐱𝐱^𝑇?
4. Create a 5×5 identity matrix 𝐈 and print it.