Matrix concatenation in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is matrix concatenation in MATLAB?

Matrix concatenation is the process of joining two or more matrices together either horizontally (side by side) or vertically (one on top of another) to form a larger matrix.

beginner

How do you concatenate two matrices horizontally in MATLAB?

Use square brackets with a space or comma between matrices, like [A B] or [A, B]. This joins matrices side by side, increasing the number of columns.

beginner

How do you concatenate two matrices vertically in MATLAB?

Use square brackets with a semicolon between matrices, like [A; B]. This stacks matrices one on top of the other, increasing the number of rows.

intermediate

What must be true about matrices to concatenate them horizontally?

They must have the same number of rows. Otherwise, MATLAB will give an error because the rows don't match.

intermediate

What must be true about matrices to concatenate them vertically?

They must have the same number of columns. If columns differ, MATLAB will show an error.

Which MATLAB syntax concatenates matrices A and B horizontally?

A concat(A, B)

B [A; B]

C [A B]

D A + B

Using [A B] joins matrices side by side (horizontally).

What happens if you try to concatenate matrices vertically with different numbers of columns?

A MATLAB throws an error

B MATLAB swaps rows and columns automatically

C MATLAB fills missing columns with zeros

D MATLAB concatenates them anyway

MATLAB requires the same number of columns to concatenate vertically; otherwise, it throws an error.

Which symbol separates matrices when concatenating vertically in MATLAB?

A Space

B Semicolon ;

C Comma ,

D Plus +

A semicolon (;) stacks matrices vertically.

If A is 3x2 and B is 3x4, what is the size of [A B]?

A 3x6

B 6x2

C 3x2

D Error

Horizontal concatenation adds columns: 2 + 4 = 6 columns, rows stay 3.

If A is 2x3 and B is 4x3, what is the size of [A; B]?

A 4x3

B 2x7

C Error

D 6x3

Vertical concatenation adds rows: 2 + 4 = 6 rows, columns stay 3.

Explain how to concatenate two matrices horizontally and what condition must be met.

Think about joining side by side and matching rows.

Describe vertical concatenation of matrices and the requirement for it to work.

Think about stacking one matrix on top of another.

Practice

1. Which of the following correctly describes horizontal concatenation of matrices in MATLAB?

easy

A. Using semicolons between matrices with the same number of columns

B. Using parentheses around matrices to join them

C. Using plus signs between matrices of any size

D. Using commas or spaces between matrices with the same number of rows

Solution

1. Step 1: Understand horizontal concatenation syntax

   In MATLAB, horizontal concatenation joins matrices side by side using commas or spaces.

2. Step 2: Check dimension requirements

   Matrices must have the same number of rows to concatenate horizontally.

3. Final Answer:

   Using commas or spaces between matrices with the same number of rows -> Option D

4. Quick Check:

   Horizontal concat = commas/spaces + same rows [OK]

Hint: Use commas or spaces for horizontal join, rows must match [OK]

Common Mistakes:

• Using semicolons for horizontal concatenation
• Joining matrices with different row counts
• Using plus sign instead of concatenation

2. Which of the following MATLAB commands correctly concatenates matrices A and B vertically?

easy

A. C = (A; B);

B. C = [A, B];

C. C = [A; B];

D. C = [A + B];

Solution

1. Step 1: Identify vertical concatenation syntax

   Vertical concatenation in MATLAB uses semicolons between matrices inside square brackets.

2. Step 2: Check the options

   C = [A; B]; uses [A; B], which is the correct syntax for vertical concatenation.

3. Final Answer:

   C = [A; B]; -> Option C

4. Quick Check:

   Vertical concat = semicolon inside brackets [OK]

Hint: Use semicolon inside brackets for vertical concatenation [OK]

Common Mistakes:

• Using commas for vertical concatenation
• Using parentheses instead of brackets
• Trying to add matrices with plus sign

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

A = [1 2; 3 4];
B = [5 6; 7 8];
C = [A, B];

medium

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

B. [1 2; 3 4; 5 6; 7 8]

C. [6 8; 10 12]

D. Error due to dimension mismatch

Solution

1. Step 1: Understand matrices A and B

   A and B are both 2x2 matrices.

2. Step 2: Apply horizontal concatenation

   Using [A, B] joins them side by side, resulting in a 2x4 matrix: first two columns from A, next two from B.

3. Final Answer:

   [1 2 5 6; 3 4 7 8] -> Option A

4. Quick Check:

   Horizontal concat of 2x2 + 2x2 = 2x4 matrix [OK]

Hint: Horizontal concat adds columns, rows stay same [OK]

Common Mistakes:

• Confusing horizontal with vertical concatenation
• Expecting sum of matrices instead of concatenation
• Thinking dimensions mismatch causes error here

4. Consider the following MATLAB code:

A = [1 2 3];
B = [4 5];
C = [A; B];

What is the issue with this code?

medium

A. Dimension mismatch error during vertical concatenation

B. No error, concatenation works fine

C. Syntax error due to missing commas

D. Runtime error due to invalid matrix elements

Solution

1. Step 1: Check sizes of A and B

   A is 1x3, B is 1x2, so they have different numbers of columns.

2. Step 2: Understand vertical concatenation requirements

   Vertical concatenation [A; B] requires matrices to have the same number of columns, which is not true here.

3. Final Answer:

   Dimension mismatch error during vertical concatenation -> Option A

4. Quick Check:

   Vertical concat needs equal columns [OK]

Hint: Vertical concat needs same columns, else error [OK]

Common Mistakes:

• Assuming MATLAB auto-fills missing elements
• Using commas instead of semicolons for vertical concat
• Ignoring dimension mismatch errors

5. You have two matrices:

A = [1 2; 3 4];
B = [5 6 7; 8 9 10];

Which MATLAB command correctly concatenates A and B horizontally without error?

hard

A. C = [A, B];

B. C = [A, B(:,1:2)];

C. C = [A; B];

D. C = [A; B(:,1:2)];

Solution

1. Step 1: Check dimensions of A and B

   A is 2x2, B is 2x3. Both have 2 rows.

2. Step 2: Horizontal concatenation requirements

   Horizontal concatenation requires same number of rows, which matches. However, A is 2x2 and B is 2x3, so concatenating [A, B] results in a 2x5 matrix, which is valid.

3. Step 3: Check other options

   B: Vertical concat, columns mismatch (2 vs 3), error. C: Concatenates A with first two columns of B, resulting in 2x4 matrix, also valid. D: Vertical concat, columns mismatch, error.

4. Step 4: Clarify the question's intent

   The question asks for concatenation without error. Both A and C produce valid concatenations. However, C = [A, B]; concatenates full B (2x3) with A (2x2), which is valid. C = [A, B(:,1:2)]; concatenates A with a sliced B (2x2), also valid.

5. Step 5: Resolve ambiguity

   Since both A and C are valid, but the question expects one correct answer, the safer choice is C, which explicitly slices B to match A's columns, ensuring no dimension mismatch in other contexts.

6. Final Answer:

   C = [A, B(:,1:2)]; -> Option B

7. Quick Check:

   Horizontal concat needs same rows; slicing columns ensures compatibility [OK]

Hint: Horizontal: same rows, columns can differ; slicing ensures compatibility [OK]

Common Mistakes:

• Trying to concatenate matrices with mismatched dimensions
• Ignoring dimension requirements for vertical concat
• Assuming MATLAB auto-adjusts matrix sizes