Row and column vectors in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a row vector in MATLAB?

A row vector is a 1-by-n matrix, meaning it has 1 row and multiple columns. For example, [1 2 3] is a row vector with 3 elements.

beginner

What is a column vector in MATLAB?

A column vector is an n-by-1 matrix, meaning it has multiple rows and 1 column. For example, [1; 2; 3] is a column vector with 3 elements.

beginner

How do you create a row vector with elements 4, 5, and 6 in MATLAB?

You write the elements separated by spaces or commas inside square brackets: v = [4 5 6];

beginner

How do you create a column vector with elements 4, 5, and 6 in MATLAB?

You write the elements separated by semicolons inside square brackets: v = [4; 5; 6];

beginner

What is the difference between a row vector and a column vector in MATLAB?

A row vector has one row and many columns, written as [a b c]. A column vector has many rows and one column, written as [a; b; c]. They look different and behave differently in operations.

Which of the following is a row vector in MATLAB?

A [1; 2; 3]

B [1 2 3]

C [1, 2; 3, 4]

D [1; 2, 3]

A row vector has elements in one row separated by spaces or commas: [1 2 3].

How do you separate elements to create a column vector in MATLAB?

A With spaces

B With commas

C With semicolons

D With periods

Semicolons separate rows, so [1; 2; 3] creates a column vector.

What is the size of a row vector with 5 elements?

A 1-by-5

B 5-by-1

C 5-by-5

D 1-by-1

A row vector with 5 elements has 1 row and 5 columns, so size is 1-by-5.

What is the size of a column vector with 4 elements?

A 1-by-1

B 1-by-4

C 4-by-4

D 4-by-1

A column vector with 4 elements has 4 rows and 1 column, so size is 4-by-1.

Which MATLAB code creates a column vector?

A v = [7; 8; 9];

B v = [7 8 9];

C v = [7, 8, 9];

D v = [7 8; 9 10];

Using semicolons creates a column vector: [7; 8; 9].

Explain how to create row and column vectors in MATLAB and how they differ.

Think about how elements are separated inside square brackets.

Describe the size (dimensions) of row and column vectors and why it matters.

Remember rows and columns count.

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