# Math 315

## Linear Algebra and Differential Equations

## Homework Hints

### Assignment 4

**3.7.6**
Augment the matrix with the 3 by 3 identity matrix.

**3.7.12**
You can use both `inv`

and `rref`

to gain insight
on this problem.

**3.8.7**
Set up the coefficient matrix for the general system of equations
and solve it.

**3.8.8**
x is a ratio of two determinants

**4.1.12**
If you let x(t) = T(t) - T_m,
then dx/dt = dT/dt.

**4.1.14**
The final principle after half a year of compounding continuously at the first rate
is the initial principal for the growth which occurs compounding continuously
at the second rate for the second half of the year.

**4.1.22**
Solve the exponential growth equation
with the initial condition x(0) = 250.
Then find t for which x(t) = 400.

**4.2.6**
The derivative at point (t,x) is x+t.

**4.2.16**
Compare numerical results with analytical results.

**4.2.18**
Notice from the line field the wide variety
of possible curve shapes which can appear.

Last modified: February 4, 2000

Bret Larget,
larget@mathcs.duq.edu