Row and column vectors in MATLAB

Introduction

Row and column vectors help organize numbers in a line horizontally or vertically. They make math with lists of numbers easy.

When you want to store a list of numbers in one row.

When you need to perform matrix math with vertical lists.

When you want to input data for plotting in MATLAB.

When you want to organize data for calculations like sums or averages.

Syntax

MATLAB

Row vector: rowVec = [1 2 3 4];
Column vector: colVec = [1; 2; 3; 4];

Use spaces or commas to separate elements in a row vector.

Use semicolons to separate elements in a column vector.

Examples

This creates a row vector with four numbers in one horizontal line.

MATLAB

rowVec = [5 10 15 20];

This creates a column vector with four numbers stacked vertically.

MATLAB

colVec = [5; 10; 15; 20];

You can also use commas to separate elements in a row vector.

MATLAB

rowVec = [1, 2, 3, 4];

Sample Program

This program creates a row vector and a column vector, then prints them to show their shapes.

MATLAB

rowVec = [1 2 3 4];
colVec = [1; 2; 3; 4];

% Display the vectors
disp('Row vector:');
disp(rowVec);
disp('Column vector:');
disp(colVec);

Important Notes

Row vectors look like a horizontal list: [a b c].

Column vectors look like a vertical list: [a; b; c].

You can convert between them using the transpose operator: rowVec' becomes a column vector.

Summary

Row vectors store numbers horizontally using spaces or commas.

Column vectors store numbers vertically using semicolons.

They are basic building blocks for math and data in MATLAB.

Practice

1. Which of the following correctly creates a row vector in MATLAB?

easy

A. v = (1, 2, 3, 4);

B. v = [1 2 3 4];

C. v = [1; 2; 3; 4];

D. v = {1 2 3 4};

Solution

1. Step 1: Understand row vector syntax

   Row vectors use square brackets with spaces or commas between elements.

2. Step 2: Identify correct option

   v = [1 2 3 4]; uses spaces inside square brackets, which is correct for a row vector.

3. Final Answer:

   v = [1 2 3 4]; -> Option B

4. Quick Check:

   Row vector = horizontal elements in [ ] [OK]

Hint: Row vectors use spaces or commas inside [ ] [OK]

Common Mistakes:

• Using semicolons creates a column vector, not a row vector
• Using parentheses instead of square brackets
• Using curly braces creates a cell array, not a vector

2. Which of the following is the correct syntax to create a column vector with elements 5, 6, and 7 in MATLAB?

easy

A. v = [5 6 7];

B. v = (5; 6; 7);

C. v = [5; 6; 7];

D. v = {5; 6; 7};

Solution

1. Step 1: Recall column vector syntax

   Column vectors use square brackets with semicolons separating elements vertically.

2. Step 2: Find the option matching this syntax

   v = [5; 6; 7]; uses semicolons inside square brackets, which is correct for a column vector.

3. Final Answer:

   v = [5; 6; 7]; -> Option C

4. Quick Check:

   Column vector = vertical elements separated by ; [OK]

Hint: Use semicolons inside [ ] for column vectors [OK]

Common Mistakes:

• Using spaces instead of semicolons creates a row vector
• Using parentheses instead of square brackets
• Using curly braces creates a cell array, not a vector

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

v = [10 20 30];
size_v = size(v);

medium

A. [1 1]

B. [3 1]

C. [3 3]

D. [1 3]

Solution

1. Step 1: Understand the vector shape

   v is defined with spaces inside [ ], so it is a row vector with 1 row and 3 columns.

2. Step 2: Apply size function

   size(v) returns the dimensions as [number_of_rows number_of_columns], which is [1 3].

3. Final Answer:

   [1 3] -> Option D

4. Quick Check:

   Row vector size = [1 number_of_elements] [OK]

Hint: Row vector size is 1 row and number of columns [OK]

Common Mistakes:

• Confusing row and column vector sizes
• Expecting size to return number of elements only
• Mixing up output format of size function

4. Identify the error in the following MATLAB code that tries to create a column vector:

v = [1, 2; 3, 4];

medium

A. The vector is actually a 2x2 matrix, not a column vector.

B. The commas should be replaced with semicolons.

C. Square brackets cannot be used for vectors.

D. The semicolon at the end is missing.

Solution

1. Step 1: Analyze the matrix dimensions

   The code uses commas and semicolons inside [ ], which creates a 2x2 matrix, not a column vector.

2. Step 2: Understand column vector requirements

   A column vector must have one column and multiple rows, but this code has 2 rows and 2 columns.

3. Final Answer:

   The vector is actually a 2x2 matrix, not a column vector. -> Option A

4. Quick Check:

   Mixed commas and semicolons create matrices, not vectors [OK]

Hint: Commas separate columns; semicolons separate rows [OK]

Common Mistakes:

• Thinking commas separate rows
• Assuming semicolons are optional for columns
• Confusing matrix with vector shapes

5. You want to create a 1x5 row vector with elements from 1 to 5, then convert it to a 5x1 column vector. Which MATLAB code correctly does this?

hard

A. rowVec = [1 2 3 4 5];
colVec = rowVec';

B. rowVec = [1; 2; 3; 4; 5];
colVec = rowVec;

C. rowVec = [1 2 3 4 5];
colVec = rowVec(:)';

D. rowVec = [1 2 3 4 5];
colVec = rowVec;

Solution

1. Step 1: Create a row vector

   rowVec = [1 2 3 4 5]; creates a 1x5 row vector using spaces inside square brackets.

2. Step 2: Convert row vector to column vector

   Using the transpose operator (') converts the row vector to a 5x1 column vector.

3. Final Answer:

   rowVec = [1 2 3 4 5]; colVec = rowVec'; -> Option A

4. Quick Check:

   Transpose operator ' flips row to column vector [OK]

Hint: Use ' (transpose) to switch row to column vector [OK]

Common Mistakes:

• Using semicolons inside row vector definition
• Forgetting to transpose to get column vector
• Assuming rowVec = colVec creates column vector