Row and column vectors in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this MATLAB code?

Consider the following MATLAB code that creates a row vector and a column vector. What will be the size of B after execution?

MATLAB

A = [1, 2, 3, 4];
B = A';

A 4 1

B 4 4

C 1 4

D 1 1

💡 Hint

Remember that the apostrophe (') operator transposes the vector.

The vector A is a row vector with size 1x4. Transposing it with ' converts it into a column vector with size 4x1.

❓ Predict Output

intermediate

What is the output of this MATLAB code?

What will be the output of the following code snippet?

MATLAB

v = [5; 10; 15];
result = v(2);

A 5

B 10

C Error: Index exceeds matrix dimensions.

D 15

💡 Hint

Indexing in MATLAB starts at 1 and works down the column for column vectors.

The vector v is a column vector with elements 5, 10, and 15. Accessing v(2) returns the second element, which is 10.

❓ Predict Output

advanced

What is the output of this MATLAB code involving vector multiplication?

Given the row vector r = [1 2 3] and column vector c = [4; 5; 6], what is the result of r * c?

MATLAB

r = [1 2 3];
c = [4; 5; 6];
result = r * c;

A 32

B [4 10 18]

C [4; 10; 18]

D Error: Inner matrix dimensions must agree.

💡 Hint

Matrix multiplication rules: number of columns in first must equal number of rows in second.

r is 1x3 and c is 3x1, so multiplication is valid and results in a 1x1 scalar: 1*4 + 2*5 + 3*6 = 32.

❓ Predict Output

advanced

What error does this MATLAB code produce?

What error will this code produce?

MATLAB

r = [1 2 3];
c = [4 5 6];
result = r * c;

A [4 10 18]

B 18

C Error: Inner matrix dimensions must agree.

D Error: Undefined function or variable 'result'.

💡 Hint

Check the dimensions of the vectors for matrix multiplication.

Both r and c are 1x3 row vectors. Multiplying two 1x3 matrices is invalid because the inner dimensions do not match.

🧠 Conceptual

expert

How many elements are in the resulting vector?

If you create a row vector R = 1:7 and a column vector C = (1:7)', what is the number of elements in the vector V = R + C'?

A 49

B Error: Matrix dimensions must agree.

C 1

D 7

💡 Hint

Check the dimensions of R, C, and C' before addition.

R is a 1x7 row vector, C is a 7x1 column vector, so C' is 1x7 row vector. Adding two 1x7 vectors results in a 1x7 vector with 7 elements.

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