Solving A System Of Linear Equations Using Matrices - Sharp EL-9650 Handbook

Solving a System of Linear Equations Using Matrices

Each system of three linear equations consists of three variables. Equations in more than
three variables cannot be graphed on the graphing calculator. The solution of the system of
equations can be found numerically using the Matrix feature or the System solver in the
Tool feature.
A system of linear equations can be expressed as AX = B (A, X and B are matrices). The
solution matrix X is found by multiplying A
and the correct answer will be obtained by multiplying BA
matrix that when multiplied by A results in the identity matrix I (A
matrix I is defined to be a square matrix (n x n) where each position on the diagonal is 1
and all others are 0.
Example
Use matrix multiplication to solve a system of linear equations.
1.
Enter the 3 x 3 identity matrix in matrix A.
2.
Find the inverse matrix of the matrix B.
3.
Solve the equation system.
{
x + 2y + z = 8
2x + y - z = 1
x + y - 2z = -3
Before
There may be differences in the results of calculations and graph plotting depending on the setting.
Starting
Return all settings to the default value and delete all data.
Step & Key Operation
*Use either pen touch or cursor to operate.
1
1
Set up 3 x 3 identity matrix at the
-
home screen.
C
MATRIX
*
1
2
-
Save the identity matrix in matrix A.
STO A
MATRIX
*
1
3
Confirm that the identity matrix is
-
stored in matrix A.
B 1
MATRIX
* *
-1 B. Note that the multiplication is "order sensitive"
0 5 3
ENTER
*
1
ENTER
*
EL-9650/9600c Graphing Calculator
. An inverse matrix A
-1
B
1 2 1
2 1 -1
1 1 -2
Display
is a
-1
x A=I). The identity
-1
Notes
6-2