Matrix rank and null space in MATLAB - Mini Project: Build & Apply

Matrix rank and null space

📖 Scenario: You are working with a small company that needs to analyze a matrix representing some data relationships. Understanding the matrix's rank and null space will help them see how many independent relationships exist and what combinations lead to zero.

🎯 Goal: Build a MATLAB script that creates a matrix, calculates its rank, finds its null space, and displays these results clearly.

📋 What You'll Learn

Create a matrix variable named A with specific values

Create a variable named threshold to use as a tolerance for rank calculation

Calculate the rank of matrix A using the rank function with threshold

Calculate the null space of matrix A using the null function

Display the rank and null space results using disp

💡 Why This Matters

🌍 Real World

Matrix rank and null space are important in engineering and data science to understand system dependencies and solutions to linear equations.

💼 Career

Knowing how to compute rank and null space helps in fields like control systems, signal processing, and machine learning where matrix properties matter.

1

Create the matrix A

Create a matrix called A with these exact values: [1 2 3; 4 5 6; 7 8 9]

MATLAB

% Create the matrix A with the given values
% Your code here

Need a hint?

Use square brackets [] to create the matrix and separate rows with semicolons.

2

Set the rank threshold

Create a variable called threshold and set it to 1e-10 to use as the tolerance for rank calculation

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
% Create the threshold variable for rank tolerance
% Your code here

Need a hint?

Use scientific notation 1e-10 to set a very small tolerance value.

3

Calculate the rank and null space

Calculate the rank of A using rank(A, threshold) and store it in r. Then calculate the null space of A using null(A) and store it in nspace

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
threshold = 1e-10;
% Calculate the rank and null space
% Your code here

Need a hint?

Use the rank function with two inputs and the null function with one input.

4

Display the results

Use disp to print the text 'Rank of A:' followed by the value of r. Then use disp to print the text 'Null space of A:' followed by the matrix nspace

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
threshold = 1e-10;
r = rank(A, threshold);
nspace = null(A);
% Display the rank and null space
% Your code here

Need a hint?

Use disp twice: once for the rank label and value, once for the null space label and matrix.