# Lesson 3: Looking at more specialized elements

Convert these questions from the "paper-pencil" format to PrairieLearn.

## Example 1:

Given a matrix $A$ and a vector $b$, compute the matrix-vector multiplication $y = Ab$

Consider:

• $A$ and $b$ are randomized
• How do you want to provide (display) the matrices? Take a look at pl-variable-output, pl-matrix-latex and pl-python-variable.
• How do you want students to submit their answers? Take a look at pl-matrix-component-input and pl-matrix-input.

PrairieLearn implementation:

## Example 2:

Consider the Standard I-beam cross-section: The table below has the geometric properties for different specifications for a steel beam: For the S20 x 66 beam, what is the maximum normal stress $\sigma_x$ assuming that the maximum moment is equal to $M_{max} = 5 \times 10^5 \rm\ lb \cdot in$.

Solution:

For the S20 x 66 beam, we use $I_x = 1190 \rm\ in^4$ and $c = h/2 = 10 \rm\ in$. Hence the maximum normal stress is:

$$\sigma_x = \frac{M_{max} \,c}{I_x} = 0.042 \times 10^5 \rm\ lb/in^2 = 4.2 \rm\ ksi$$

Take one step further:

• provide random choice for the beam designations
• think about the different ways you can present the table information

PrairieLearn implementation:

## Example 3:

Convert an integer number $x$ from decimal representation (base 10) to binary representation (base 2).

You can use pl-multiple-choice for this question. If you want to have the student input the answer, you can utilize pl-string-input.

PrairieLearn implementation:

## Example 4:

For given values of X, Y and Z, determine F. You can use pl-overlay to add the input boxes on top of the image.

PrairieLearn implementation:

## Homework 3

Create new questions using some of the elements discussed today:

pl-matrix-component-input documentation and example

pl-matrix-input documentation and example

pl-matrix-latex documentation and example

pl-variable-output documentation and example

pl-python-variable documentation and example

pl-string-input documentation and example

pl-overlay documentation and example