Special matrices (zeros, ones, eye, rand) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of zeros and ones matrix operations

What is the output of the following MATLAB code?

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

MATLAB

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

A [1 1; 1 1]

B [3 3; 3 3]

C Error: Matrix dimensions must agree.

D [0 0; 0 0]

💡 Hint

Remember that zeros multiplied by any number results in zeros.

Matrix A is 2x3 zeros, B is 3x2 ones. Multiplying zeros by ones results in a 2x2 zero matrix.

❓ Predict Output

intermediate

Eye matrix diagonal values

What does the following MATLAB code display?

 I = eye(4);
 disp(I(2,2));
 disp(I(2,3));

MATLAB

I = eye(4);
disp(I(2,2));
disp(I(2,3));

A

0
1

B

1
1

C

1
0

D

0
0

💡 Hint

Eye matrix has ones on the diagonal and zeros elsewhere.

I(2,2) is on the diagonal, so it is 1. I(2,3) is off-diagonal, so it is 0.

🔧 Debug

advanced

Identify the error in matrix creation

What error does this MATLAB code produce?

 M = zeros(3);
 N = ones(2,3);
 P = M + N;

MATLAB

M = zeros(3);
N = ones(2,3);
P = M + N;

A No error, P is a 3x3 matrix of ones.

B Error: Matrix dimensions must agree.

C Error: Undefined function or variable 'P'.

D No error, P is a 2x3 matrix of zeros.

💡 Hint

Check the sizes of M and N before adding.

M is 3x3, N is 2x3, so addition is invalid due to dimension mismatch.

❓ Predict Output

advanced

Random matrix value range

What is the range of values produced by this MATLAB code?

 R = rand(2,2);
 disp(min(R(:)));
 disp(max(R(:)));

MATLAB

R = rand(2,2);
disp(min(R(:)));
disp(max(R(:)));

A Values between 0 and 1, exclusive

B Values between 0 and 1, inclusive

C Values between -1 and 1

D Values between 1 and 2

💡 Hint

rand generates numbers in the interval (0,1).

rand produces uniformly distributed random numbers strictly greater than 0 and less than 1.

🧠 Conceptual

expert

Number of elements in special matrices

How many elements does the matrix created by eye(5,3) contain in MATLAB?

A 15

B 5

C 3

D 8

💡 Hint

Count total elements in a 5-by-3 matrix.

eye(5,3) creates a 5 rows by 3 columns matrix, so total elements = 5*3 = 15.

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