Computation with Sage

Driving row reduction through a computer algebra system, so systems with hundreds of equations become as routine as small ones.

Understanding Linear Algebra, Computation with Sage

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4 exercises

Activity 1.3.2

Enter the following matrix into Sage.

Give the matrix the name $A$ by entering
```
A = matrix( ..., ..., [ ... ])
	      
```
We may then find its reduced row echelon form by entering
```
A = matrix( ..., ..., [ ... ])
A.rref()
	      
```
A common mistake is to forget the parentheses after rref.
Use Sage to find the reduced row echelon form of the matrix from this item of this activity.
Use Sage to describe the solution…

2.5

Exercise 1

Consider the linear system Write this system as an augmented matrix and use Sage to find a description of the solution space.

2.5

Exercise 4

The fuel inside model rocket motors is a black powder mixture that ideally consists of 60% charcoal, 30% potassium nitrate, and 10% sulfur by weight.

Suppose you work at a company that makes model rocket motors. When you come into work one morning, you learn that yesterday's first shift made a perfect batch of fuel. The second shift, however, misread the recipe and used 50% charcoal, 20% potassium…

2.5

Exercise 5

This exercise is about balancing chemical reactions.

Chemists denote a molecule of water as $\text{H}_2\text{O}$ , which means it is composed of two atoms of hydrogen (H) and one atom of oxygen (O). The process by which hydrogen burns is described by the chemical reaction This means that $x$ molecules of hydrogen $\text{H}_2$ combine with $y$ molecules of oxygen $\text{O}_2$ to produce $z$ water molecules. The number of hydrogen atoms is the sa…

2.5