# Math 315

## Linear Algebra and Differential Equations

## Homework Hints

### Assignment 2

**2.4.4**
Think about what the reduced row echelon form of the matrix will be.
The rank is equal to the number of nonzero rows.
The number of solutions will depend on whether the system is consistent or not.

**2.4.10**
Interpret the output correctly from `rref`

.

**3.1.12**
Write the matrix A as a two-by-two matrix with four unknowns.
The matrix multiplications give you four linear equations in four unknowns.
Solve these by any method.

**3.1.18**
Write out nine linear equations in nine unknowns.
Use MATLAB to solve this large system.
(Once you've learned about inverse matrices,
you will know an easier way to find the answer.)

**3.2.6**
It will be two times a matrix that rotates the plane clockwise by 90 degrees.
Clockwise 90 degrees is a rotation of 3*pi/2 counterclockwise.

**3.2.8**
Hint. x maps to -x while y maps to y.

**3.2.12**
This is a simple generalization of the example in lecture
that projects points in the plane onto the x axis.

**3.2.24**
Try this with the dog shape with the map function.
Dog meets bulldozer is the result.
(Sorry all dog lovers, including Dr. Taylor.)

Last modified: January 24, 2000

Bret Larget,
larget@mathcs.duq.edu