Matrix creation in MATLAB

Introduction

We create matrices to organize numbers or data in rows and columns. This helps us work with many values at once, like a table.

When you want to store a grid of numbers, like a game board or a spreadsheet.

When you need to perform math on multiple values together, like adding or multiplying sets of numbers.

When you want to represent images or data in rows and columns.

When you want to solve systems of equations using arrays of numbers.

Syntax

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];

Use square brackets [ ] to create a matrix.

Separate elements in the same row with spaces or commas.

Use semicolons ; to start a new row.

Examples

This creates a 3x3 matrix with 3 rows and 3 columns.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];

A 2x2 matrix using commas to separate elements in a row.

MATLAB

B = [10, 20; 30, 40];

Creates a 2x3 matrix filled with zeros.

MATLAB

C = zeros(2,3);

Creates a 3x3 identity matrix (ones on the diagonal, zeros elsewhere).

MATLAB

D = eye(3);

Sample Program

This program creates three matrices: a 3x3 matrix A, a 2x3 zero matrix B, and a 3x3 identity matrix C. It then displays each matrix.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
disp('Matrix A:');
disp(A);

B = zeros(2,3);
disp('Matrix B (zeros):');
disp(B);

C = eye(3);
disp('Matrix C (identity):');
disp(C);

Important Notes

You can create matrices with different sizes by changing the number of rows and columns.

Use functions like zeros, ones, and eye to quickly create special matrices.

Remember that MATLAB indexes matrices starting at 1, not 0.

Summary

Matrices are made using square brackets with spaces or commas for columns and semicolons for rows.

Special functions help create common matrices like zeros and identity matrices.

Matrices let you organize and work with many numbers easily.

Practice

1. Which of the following correctly creates a 2x3 matrix in MATLAB?

easy

A. [1 2; 3 4 5]

B. [1, 2; 3, 4; 5, 6]

C. [1 2 3; 4 5 6]

D. [1; 2; 3; 4]

Solution

1. Step 1: Understand matrix dimensions

   A 2x3 matrix has 2 rows and 3 columns.

2. Step 2: Check each option's shape

   [1 2 3; 4 5 6] has 2 rows separated by semicolon and 3 columns separated by spaces, so it is 2x3.

3. Final Answer:

   [1 2 3; 4 5 6] -> Option C

4. Quick Check:

   2 rows and 3 columns = [1 2 3; 4 5 6] [OK]

Hint: Rows separated by semicolons, columns by spaces or commas [OK]

Common Mistakes:

• Using commas instead of semicolons for rows
• Mismatched number of columns in rows
• Confusing rows and columns

2. Which MATLAB code correctly creates a 3x3 identity matrix?

easy

A. eye(3)

B. zeros(3,3)

C. ones(3)

D. diag(3)

Solution

1. Step 1: Recall identity matrix function

   In MATLAB, eye(n) creates an n-by-n identity matrix.

2. Step 2: Check options

   eye(3) uses eye(3), which is the correct function for a 3x3 identity matrix.

3. Final Answer:

   eye(3) -> Option A

4. Quick Check:

   Identity matrix = eye(3) [OK]

Hint: Use eye(n) for identity matrix of size n [OK]

Common Mistakes:

• Using zeros or ones instead of eye
• Using diag with incorrect vector size
• Confusing identity with zero matrix

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

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

medium

A. [1 2; 3 4; 0 0 0]

B. [1 2 0 0 0; 3 4 0 0 0]

C. [1 2; 3 4; 0 0]

D. Error: Matrix dimensions must agree.

Solution

1. Step 1: Understand matrix sizes

   A is 2x2, B is 2x3 of zeros.

2. Step 2: Concatenate horizontally

   [A B] joins matrices side by side, resulting in 2 rows and 5 columns.

3. Final Answer:

   [1 2 0 0 0; 3 4 0 0 0] -> Option B

4. Quick Check:

   Horizontal concat of 2x2 and 2x3 = 2x5 matrix [OK]

Hint: Horizontal concat needs same row count [OK]

Common Mistakes:

• Trying to concat matrices with different row counts vertically
• Confusing zeros size
• Expecting error instead of valid concat

4. Identify the error in this MATLAB code:

M = [1 2 3; 4 5];

medium

A. Missing semicolon between rows

B. Matrix elements must be separated by commas

C. Use parentheses instead of square brackets

D. Rows have different number of columns

Solution

1. Step 1: Check matrix row sizes

   First row has 3 elements, second row has 2 elements.

2. Step 2: Understand MATLAB matrix rules

   All rows must have the same number of columns; here they differ.

3. Final Answer:

   Rows have different number of columns -> Option D

4. Quick Check:

   Matrix rows must match column count [OK]

Hint: All rows must have equal columns in matrix [OK]

Common Mistakes:

• Thinking commas are required between rows
• Using parentheses instead of brackets
• Ignoring unequal row lengths

5. You want to create a 4x4 matrix with 1s on the diagonal and 0.5 everywhere else. Which MATLAB code achieves this?

hard

A. M = 0.5*ones(4); M(eye(4) == 1) = 1;

B. M = eye(4) + 0.5;

C. M = 0.5*ones(4) + eye(4);

D. M = ones(4); M(eye(4) == 1) = 0.5;

Solution

1. Step 1: Create a 4x4 matrix of 0.5

   Using 0.5*ones(4) sets all elements to 0.5.

2. Step 2: Replace diagonal elements with 1

   Using logical indexing M(eye(4) == 1) = 1; sets diagonal to 1.

3. Final Answer:

   M = 0.5*ones(4); M(eye(4) == 1) = 1; -> Option A

4. Quick Check:

   Diagonal 1, others 0.5 = M = 0.5*ones(4); M(eye(4) == 1) = 1; [OK]

Hint: Set all to 0.5 then replace diagonal with 1 [OK]

Common Mistakes:

• Adding eye(4) instead of replacing diagonal
• Mixing addition and multiplication incorrectly
• Setting diagonal to 0.5 instead of 1