Special matrices (zeros, ones, eye, rand) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 3x3 matrix of zeros.

MATLAB

A = [1](3, 3);

Drag options to blanks, or click blank then click option'

Arand

Bones

Czeros

Deye

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ones' instead of 'zeros' will create a matrix filled with ones.

Using 'eye' creates an identity matrix, not zeros.

The zeros function creates a matrix filled with zeros. Here, zeros(3, 3) creates a 3x3 matrix of zeros.

2fill in blank

medium

Complete the code to create a 4x4 identity matrix.

MATLAB

I = [1](4);

Drag options to blanks, or click blank then click option'

Aones

Beye

Czeros

Drand

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ones' creates a matrix full of ones, not an identity matrix.

Using 'zeros' creates a matrix full of zeros.

The eye function creates an identity matrix. eye(4) creates a 4x4 identity matrix with ones on the diagonal and zeros elsewhere.

3fill in blank

hard

Fix the error in the code to create a 2x5 matrix of random numbers between 0 and 1.

MATLAB

R = [1](2, 5);

Drag options to blanks, or click blank then click option'

Arand

Beye

Czeros

Dones

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ones' or 'zeros' creates matrices with fixed values, not random.

Using 'eye' creates an identity matrix, which is square and not random.

The rand function creates a matrix of random numbers between 0 and 1. rand(2, 5) creates a 2x5 matrix with random values.

4fill in blank

hard

Fill both blanks to create a 5x5 matrix of ones and then replace the diagonal with zeros.

MATLAB

M = [1](5);
M([2]) = 0;

Drag options to blanks, or click blank then click option'

Aones

Beye

C1:6:numel(M)

Dzeros

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'eye' instead of 'ones' creates an identity matrix, not a matrix of ones.

Using 'zeros' to create the matrix will not fill it with ones first.

First, ones(5) creates a 5x5 matrix filled with ones. Then, 1:6:numel(M) selects the diagonal elements of the matrix M. Setting these to zero replaces the diagonal with zeros.

5fill in blank

hard

Fill all three blanks to create a 3x4 matrix of random numbers, then create a 4x4 identity matrix, and finally a 2x2 matrix of zeros.

MATLAB

A = [1](3, 4);
B = [2](4);
C = [3](2, 2);

Drag options to blanks, or click blank then click option'

Arand

Beye

Czeros

Dones

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up the functions and their sizes.

Using 'ones' instead of 'zeros' for the last matrix.

rand(3, 4) creates a 3x4 matrix with random numbers. eye(4) creates a 4x4 identity matrix. zeros(2, 2) creates a 2x2 matrix filled with zeros.

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