Why numerical computation solves real problems in MATLAB - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the square root of 16.

MATLAB

result = sqrt([1]);

Drag options to blanks, or click blank then click option'

A4

B16

C8

D25

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong number inside sqrt, like 25 or 8.

The sqrt function calculates the square root of the input number. Here, the square root of 16 is 4.

2fill in blank

medium

Complete the code to create a vector from 1 to 5.

MATLAB

vec = [1];

Drag options to blanks, or click blank then click option'

A1:10

Blinspace(1,10,5)

C[5 4 3 2 1]

D1:5

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1:10 creates a longer vector than needed.

The colon operator 1:5 creates a vector with values from 1 to 5.

3fill in blank

hard

Fix the error in the code to compute the sum of elements in vector v.

MATLAB

total = [1](v);

Drag options to blanks, or click blank then click option'

Asum

Badd

Cplus

Dtotal

Attempts:

3 left

💡 Hint

Common Mistakes

Using add or plus which are not functions for summing vectors.

The sum function adds all elements of the vector v.

4fill in blank

hard

Fill both blanks to create a vector of squares of numbers 1 to 5.

MATLAB

squares = ([1]:[2]).^2;

Drag options to blanks, or click blank then click option'

A1

B2

C5

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong start or end values like 2 or 10.

The colon operator 1:5 creates numbers from 1 to 5. Squaring each gives the squares vector.

5fill in blank

hard

Fill all three blanks to create a vector of even numbers from 2 to 10.

MATLAB

evens = [1]:[2]:[3];

Drag options to blanks, or click blank then click option'

A1

B2

C10

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using step 1 instead of 2, or wrong start/end values.

The syntax start:step:end creates a vector starting at 2, stepping by 2, up to 10, giving even numbers.

Practice

1.

Why do we use numerical computation in MATLAB for real-world problems?

easy

A. Because numerical computation is always faster than exact math

B. Because MATLAB cannot handle symbolic math

C. Because exact math solutions are often impossible or too complex

D. Because numerical computation gives exact answers every time

Solution

1. Step 1: Understand the nature of real-world problems

   Many real-world problems involve complex equations that cannot be solved exactly by hand or symbolic math.

2. Step 2: Role of numerical computation

   Numerical computation approximates solutions using numbers and calculations, making it possible to find answers where exact math fails.

3. Final Answer:

   Because exact math solutions are often impossible or too complex -> Option C

4. Quick Check:

   Numerical computation solves complex problems [OK]

Hint: Numerical methods approximate when exact math is too hard [OK]

Common Mistakes:

• Thinking numerical computation always gives exact answers
• Believing MATLAB cannot do symbolic math
• Assuming numerical computation is always faster

2.

Which MATLAB command correctly creates a vector of 100 linearly spaced points between 0 and 1?

?

easy

A. linspace(0, 1, 100)

B. range(0, 1, 100)

C. vector(0, 1, 100)

D. linspace(100, 0, 1)

Solution

1. Step 1: Recall MATLAB function for linear spacing

   MATLAB's linspace creates linearly spaced vectors with syntax linspace(start, end, number_of_points).

2. Step 2: Match the correct syntax

   The correct command is linspace(0, 1, 100) to get 100 points from 0 to 1.

3. Final Answer:

   linspace(0, 1, 100) -> Option A

4. Quick Check:

   linspace(start, end, n) = linspace(0,1,100) [OK]

Hint: Use linspace(start, end, count) for evenly spaced vectors [OK]

Common Mistakes:

• Using range instead of linspace
• Swapping start and end values
• Using incorrect function names like vector

3.

What is the output of this MATLAB code?

x = linspace(0, 2, 5);
y = sin(pi * x);
y

medium

A. [0 1 0 -1 0]

B. [0 0.5 1 0.5 0]

C. [0 0.7071 1 0.7071 0]

D. [0 0.7071 0 -0.7071 0]

Solution

1. Step 1: Calculate vector x values

   linspace(0, 2, 5) creates [0, 0.5, 1, 1.5, 2].

2. Step 2: Compute y = sin(pi * x)

   Calculate sin(pi*0)=0, sin(pi*0.5)=1, sin(pi*1)=0, sin(pi*1.5)=-1, sin(pi*2)=0.

3. Final Answer:

   [0 1 0 -1 0] -> Option A

4. Quick Check:

   sin(pi * linspace(0,2,5)) = [0 1 0 -1 0] [OK]

Hint: Calculate linspace values first, then apply sin(pi * x) [OK]

Common Mistakes:

• Confusing degrees and radians in sin function
• Miscomputing linspace values
• Using wrong function like cos instead of sin

4.

Identify the error in this MATLAB code snippet that tries to compute the square root of each element in vector A:

A = [4, 9, 16, 25];
B = sqrt A;

medium

A. sqrt function requires two arguments

B. Using square root on a vector is not allowed

C. Vector A should be a column vector

D. Missing parentheses around A in sqrt function

Solution

1. Step 1: Check MATLAB function syntax

   Functions require parentheses around their arguments, so sqrt A is invalid syntax.

2. Step 2: Correct the syntax

   Use sqrt(A) to compute element-wise square roots of vector A.

3. Final Answer:

   Missing parentheses around A in sqrt function -> Option D

4. Quick Check:

   Function calls need parentheses [OK]

Hint: Always use parentheses for function arguments in MATLAB [OK]

Common Mistakes:

• Omitting parentheses in function calls
• Thinking sqrt can't handle vectors
• Assuming sqrt needs multiple arguments

5.

You want to approximate the integral of f(x) = exp(-x^2) from 0 to 1 using numerical computation in MATLAB. Which approach best solves this real problem?

hard

A. Manually calculate the exact integral using symbolic math

B. Use integral(@(x) exp(-x.^2), 0, 1) to compute the numerical integral

C. Use a for loop to sum exp(-x^2) at random points without spacing

D. Approximate by taking the value at x=0.5 only

Solution

1. Step 1: Understand the integral problem

   The integral of exp(-x^2) has no simple exact formula, so numerical methods are needed.

2. Step 2: Use MATLAB's numerical integration function

   The integral function with an anonymous function handles this efficiently and accurately.

3. Final Answer:

   Use integral(@(x) exp(-x.^2), 0, 1) to compute the numerical integral -> Option B

4. Quick Check:

   Numerical integration with integral() solves complex integrals [OK]

Hint: Use integral() with function handle for numerical integration [OK]

Common Mistakes:

• Trying to find exact integral manually
• Summing values at random points without spacing
• Using a single point value as approximation