Special matrices (zeros, ones, eye, rand) in MATLAB - Mini Project: Build & Apply

Creating Special Matrices in MATLAB

📖 Scenario: You are working on a simple MATLAB project where you need to create different types of special matrices. These matrices are often used in math and engineering to start calculations or set up initial values.

🎯 Goal: Learn how to create zeros, ones, eye (identity), and rand matrices in MATLAB and display them.

📋 What You'll Learn

Create a 3x3 matrix of zeros called zeroMat

Create a 2x4 matrix of ones called oneMat

Create a 4x4 identity matrix called eyeMat

Create a 3x2 matrix of random numbers called randMat

Display all matrices using disp

💡 Why This Matters

🌍 Real World

Special matrices are used in engineering, computer graphics, and scientific computing to initialize data and perform calculations efficiently.

💼 Career

Knowing how to create and use these matrices is essential for jobs in data science, engineering, and software development involving numerical computations.

1

Create a 3x3 matrix of zeros

Create a variable called zeroMat and set it to a 3 by 3 matrix of zeros using the zeros function.

MATLAB

# Create a 3x3 matrix of zeros called zeroMat
% Your code here

Hint

Use the zeros(rows, columns) function to create a matrix filled with zeros.

2

Create a 2x4 matrix of ones

Create a variable called oneMat and set it to a 2 by 4 matrix of ones using the ones function.

MATLAB

zeroMat = zeros(3, 3);
% Create a 2x4 matrix of ones called oneMat
% Your code here

Hint

Use the ones(rows, columns) function to create a matrix filled with ones.

3

Create a 4x4 identity matrix

Create a variable called eyeMat and set it to a 4 by 4 identity matrix using the eye function.

MATLAB

zeroMat = zeros(3, 3);
oneMat = ones(2, 4);
% Create a 4x4 identity matrix called eyeMat
% Your code here

Hint

Use the eye(n) function to create an n by n identity matrix.

4

Create a 3x2 matrix of random numbers and display all matrices

Create a variable called randMat and set it to a 3 by 2 matrix of random numbers using the rand function. Then display all matrices zeroMat, oneMat, eyeMat, and randMat using disp.

MATLAB

zeroMat = zeros(3, 3);
oneMat = ones(2, 4);
eyeMat = eye(4);
% Create a 3x2 matrix of random numbers called randMat
% Display zeroMat, oneMat, eyeMat, and randMat
% Your code here

Hint

Use rand(rows, columns) to create random numbers between 0 and 1. Use disp to show each matrix with a label.

Practice

1. Which MATLAB function creates a matrix filled entirely with zeros?

easy

A. zeros

B. ones

C. eye

D. rand

Solution

1. Step 1: Understand the function purpose

   The zeros function creates a matrix where every element is zero.

2. Step 2: Compare with other functions

   ones creates all ones, eye creates identity matrix, rand creates random values.

3. Final Answer:

   zeros -> Option A

4. Quick Check:

   zeros = zeros matrix [OK]

Hint: Zeros means all elements are zero, so use zeros() [OK]

Common Mistakes:

• Confusing zeros with ones
• Thinking eye creates zeros
• Using rand for zeros

2. Which of the following is the correct syntax to create a 3x3 identity matrix in MATLAB?

easy

A. eye(3)

B. ones(3,3)

C. zeros(3,3)

D. rand(3)

Solution

1. Step 1: Recall identity matrix creation

   The eye(n) function creates an n-by-n identity matrix with ones on the diagonal.

2. Step 2: Check syntax correctness

   eye(3) correctly creates a 3x3 identity matrix. Others create different matrices.

3. Final Answer:

   eye(3) -> Option A

4. Quick Check:

   eye(3) = 3x3 identity [OK]

Hint: Identity matrix uses eye(n) syntax [OK]

Common Mistakes:

• Using ones or zeros instead of eye
• Missing parentheses
• Using rand for identity

3. What is the output of the following MATLAB code?

A = ones(2,3);
B = zeros(2,3);
C = A + B;

medium

A. [[2 2 2]; [2 2 2]]

B. [[0 0 0]; [0 0 0]]

C. [[1 1 1]; [1 1 1]]

D. Error due to size mismatch

Solution

1. Step 1: Understand matrix creation

   ones(2,3) creates a 2x3 matrix of all ones, zeros(2,3) creates a 2x3 matrix of zeros.

2. Step 2: Add matrices element-wise

   Adding ones and zeros element-wise results in the same ones matrix.

3. Final Answer:

   [[1 1 1]; [1 1 1]] -> Option C

4. Quick Check:

   ones + zeros = ones [OK]

Hint: Adding zeros keeps original values unchanged [OK]

Common Mistakes:

• Thinking addition doubles values
• Confusing matrix sizes
• Expecting error on addition

4. Identify the error in this MATLAB code:

M = zeros(3);
M(2,4) = 5;

medium

A. Matrix must be created with ones, not zeros

B. Index exceeds matrix dimensions error

C. No error, code runs fine

D. Syntax error due to missing semicolon

Solution

1. Step 1: Check matrix size

   zeros(3) creates a 3x3 matrix, so valid indices are 1 to 3 for both rows and columns.

2. Step 2: Analyze indexing

   Accessing M(2,4) tries to access column 4, which does not exist, causing an index error.

3. Final Answer:

   Index exceeds matrix dimensions error -> Option B

4. Quick Check:

   Index out of range = error [OK]

Hint: Check matrix size before indexing [OK]

Common Mistakes:

• Ignoring matrix size limits
• Thinking semicolon causes error
• Assuming zeros() creates bigger matrix

5. You want to create a 4x4 matrix with ones on the diagonal and random numbers between 0 and 1 elsewhere. Which MATLAB code achieves this?

hard

A. M = rand(4); M(eye(4) == 0) = 1;

B. M = eye(4) + rand(4) - diag(rand(4,1));

C. M = ones(4); M(eye(4) == 0) = rand(4);

D. M = rand(4); M(eye(4) == 1) = 1;

Solution

1. Step 1: Understand the goal

   Create a 4x4 matrix with random values, then set diagonal elements to 1.

2. Step 2: Analyze each option

   M = rand(4); M(eye(4) == 1) = 1; creates random 4x4 matrix, then replaces diagonal elements (where eye(4)==1) with 1, matching the requirement.

3. Final Answer:

   M = rand(4); M(eye(4) == 1) = 1; -> Option D

4. Quick Check:

   Random matrix with diagonal ones = M = rand(4); M(eye(4) == 1) = 1; [OK]

Hint: Set diagonal after random matrix creation using logical indexing [OK]

Common Mistakes:

• Adding matrices incorrectly
• Replacing wrong elements
• Using ones() instead of random values