Sharp EL9900 manual Solving a System of Linear Equations Using Matrices

EL-9900 Graphing Calculator

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-1B. Note that the multiplication is “order sensitive” and the correct answer will be obtained by multiplying BA-1. An inverse matrix A-1is a matrix that when multiplied by A results in the identity matrix I (A-1x A=I). The identity 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.			B
2. Find the inverse matrix of the matrix B.		1	2	1
	2		1	-1
3. Solve the equation system.
		1	1	-2

{x + 2y + z = 8

2x + y - z = 1 x + y - 2z = -3

Before Starting

There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default value and delete all data.

As the Matrix feature is only available on the Advanced keyboard, this section does not apply to the Basic keyboard.

Step & Key Operation Display Notes

1-1Set up 3 x 3 identity matrix at the home screen.

2nd F MATRIX C 0 5 3 ENTER

1-2Save the identity matrix in matrix A.

STO 2nd F MATRIX A 1 ENTER

1-3Confirm that the identity matrix is stored in matrix A.

2nd F MATRIX B 1

8-2