The tutor shows an example of how to solve a system of three equations using a spreadsheet.

Example: solve the system

1. -3x + 2y + z = 16
2. x – y – 3z = -19
3. 2x + y + 7z = 30

Solution:

From linear algebra, this system becomes Aq = r, where A is the matrix

-3	2	1
1	-1	-3
2	1	7

while q is the column vector

x

y

z

and r is the column vector

16

-19

30

From

Aq=r

follows

A^-1Aq=A^-1r

Furthermore, since

A^-1Aq=Iq=q

then

q=A^-1r

So we need to perform the calculation A^-1r on the spreadsheet.

My post from yesterday shows how to get A^-1 (the inverse of matrix A). It’s short, but detailed.

Assuming you’ve produced A^-1, it’s time to enter vector r:

16

-19

30

Let’s imagine, on your spreadsheet, that A^-1 resides in the range e1:g3, and that r resides in h1:h3. To multiply A^-1 by r,

1. Select a cell away from both ranges: k1, for example. Drag down to extend the selection from k1 to k3.
2. Click to the formula bar and type =mmult(e1:g3,h1:h3). Don’t press enter.
3. While holding down Ctrl and Shift, press Enter.
4. (Note): With matrices, unlike numbers, the order of the multiplication matters: in Step 2, it must be =mmult(e1:g3,h1:h3), rather than h1:h3,e1:g3.

Hopefully you see the result

-3

1

5

Therefore, x=-3, y=1, and z=5.

Source:

educ.jmu.edu

Johnson, Lee et al. Introduction to Linear Algebra. Don Mills: Addison-Wesley, 1989.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.