Colon operator for ranges in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the colon operator (:) do in MATLAB when used like this: 1:5?

It creates a row vector with values starting at 1, increasing by 1, up to 5. So, the result is [1 2 3 4 5].

beginner

How do you use the colon operator to create a vector from 2 to 10 with a step size of 2?

You write 2:2:10. This means start at 2, add 2 each time, until you reach or pass 10. The result is [2 4 6 8 10].

intermediate

What happens if the step size in the colon operator is negative, like 5:-1:1?

It creates a vector starting at 5, decreasing by 1 each time, down to 1. So, the vector is [5 4 3 2 1].

intermediate

Can the colon operator create an empty vector? If yes, give an example.

Yes. For example, 1:-1:5 creates an empty vector because starting at 1 and decreasing by 1 will never reach 5. So, the result is [].

beginner

Explain the difference between 1:5 and 1:1:5 in MATLAB.

Both create the same vector [1 2 3 4 5]. The first uses the default step size of 1, while the second explicitly sets the step size to 1.

What is the result of 3:3:12 in MATLAB?

A [3 6 9]

B [3 6 9 12]

C [3 4 5 6 7 8 9 10 11 12]

D [3 6 9 12 15]

Starting at 3, adding 3 each time until 12 gives [3 6 9 12].

What does the expression 10:-2:2 produce?

A [10 8 6 4 2]

B [10 9 8 7 6 5 4 3 2]

C [2 4 6 8 10]

D []

Starting at 10, subtracting 2 each time down to 2 results in [10 8 6 4 2].

What happens if you run 1:0:5 in MATLAB?

A []

B [1 1 1 1 1]

C [1 2 3 4 5]

D Error due to zero step size

A step size of zero is invalid and causes an error.

Which of these creates an empty vector?

A 1:1:5

B 5:1:10

C 1:-1:5

D 10:-2:2

Starting at 1 and decreasing by 1 will never reach 5, so the vector is empty.

What is the default step size when using the colon operator like 4:9?

A 1

B 0

C -1

D Depends on the numbers

If no step size is given, MATLAB uses 1 by default.

Describe how to use the colon operator to create a vector with a custom step size.

Think about how you tell MATLAB where to start, how much to jump each time, and where to stop.

Explain what happens when the step size in the colon operator does not allow reaching the end value.

Consider if the step moves away from the end value instead of towards it.

Practice

1. What does the MATLAB expression 1:5 produce?

easy

A. [1 3 5]

B. [5 4 3 2 1]

C. [1 2 3 4 5]

D. [1 2 3 4]

Solution

1. Step 1: Understand the colon operator syntax

   The expression start:end creates a sequence from start to end with step 1 by default.

2. Step 2: Apply to given expression

   Here, 1:5 means numbers from 1 to 5 increasing by 1: 1, 2, 3, 4, 5.

3. Final Answer:

   [1 2 3 4 5] -> Option C

4. Quick Check:

   1 to 5 by 1 = [1 2 3 4 5] [OK]

Hint: Colon with two numbers counts up by 1 [OK]

Common Mistakes:

• Thinking it skips numbers
• Confusing start and end order
• Assuming it counts down automatically

2. Which of the following is the correct syntax to create a vector from 10 down to 2 with step -2 in MATLAB?

easy

A. 10:-2:2

B. 10:2:-2

C. 10--2:2

D. 10:-2:-2

Solution

1. Step 1: Recall colon operator with step syntax

   The syntax is start:step:end. For counting down, step must be negative.

2. Step 2: Check each option

   10:-2:2 uses 10:-2:2, which counts down from 10 to 2 by -2 correctly.

3. Final Answer:

   10:-2:2 -> Option A

4. Quick Check:

   Descending with negative step = 10:-2:2 [OK]

Hint: Use negative step for descending ranges [OK]

Common Mistakes:

• Putting step after end value
• Using positive step for descending
• Syntax errors with double minus signs

3. What is the output of the MATLAB code:

vec = 3:3:12;

disp(vec);

medium

A. [3 4 5 6 7 8 9 10 11 12]

B. [3 6 9 12]

C. [3 6 9]

D. [12 9 6 3]

Solution

1. Step 1: Understand the colon operator with step

   The syntax start:step:end creates numbers from start to end increasing by step.

2. Step 2: Calculate the sequence

   Starting at 3, add 3 each time: 3, 6, 9, 12. Since 12 is included, the sequence ends there.

3. Final Answer:

   [3 6 9 12] -> Option B

4. Quick Check:

   3 to 12 by 3 = [3 6 9 12] [OK]

Hint: Multiply step by count until reaching or passing end [OK]

Common Mistakes:

• Stopping before including end if exact
• Confusing step with end value
• Assuming step is always 1

4. Identify the error in this MATLAB code:

range = 5:0.5:3;

medium

A. Empty vector because start > end with positive step

B. Syntax error due to decimal step

C. Vector counts down correctly

D. Step must be integer

Solution

1. Step 1: Analyze start, step, and end values

   Start is 5, end is 3, step is 0.5 (positive).

2. Step 2: Understand colon operator behavior

   With positive step, MATLAB counts up. Since 5 > 3, no values satisfy the condition, so the vector is empty.

3. Final Answer:

   Empty vector because start > end with positive step -> Option A

4. Quick Check:

   Positive step but start > end = empty vector [OK]

Hint: Step sign must match direction from start to end [OK]

Common Mistakes:

• Assuming decimal steps cause syntax errors
• Expecting vector to count down with positive step
• Thinking step must be integer

5. You want to create a vector in MATLAB that starts at 0, goes up to 1, but only includes values less than 1 with step 0.2. Which expression correctly does this?

hard

A. 0:0.2:1

B. 0:0.2:<1

C. 0:0.2:1.1

D. 0:0.2:0.9

Solution

1. Step 1: Understand the requirement

   The vector should start at 0, increase by 0.2, and include values less than 1 (not including 1).

2. Step 2: Check which end value excludes 1

   Using 0:0.2:1 includes 1 since it matches the sequence (0, 0.2, 0.4, 0.6, 0.8, 1). Since 1 is included, it violates the condition.

3. Step 3: Choose end value less than 1

   Using 0:0.2:0.9 stops at 0.8 (0.8 + 0.2 = 1.0 > 0.9), which is less than 1, so it meets the condition.

4. Final Answer:

   0:0.2:0.9 -> Option D

5. Quick Check:

   End less than 1 excludes 1 from vector [OK]

Hint: Set end value just below the limit to exclude it [OK]

Common Mistakes:

• Using end value equal to limit includes it
• Trying invalid syntax like <1
• Assuming floating point precision excludes end automatically