COEN140-Lab2: Linear Algebra Solved

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

 

Let 𝐁 = 𝐀𝐀𝑇, find the shape and rank of 𝐁

 

Let 𝐂 = 𝐀𝑇𝐀, 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 = 𝐗𝐗𝑇 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 𝐰𝑇𝐀 by coding;

 

Find the dimension of 𝐰𝑇𝐀𝐰 by coding.

 

Find a way (by coding) to verify that 𝐗𝐗𝑇 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 𝐱𝐱𝑇 by coding. What do you think is the rank of 𝐱𝐱𝑇?

 

 

4.      Create a 5×5 identity matrix 𝐈 and print it.