HP HP-28S - Solving a System of Linear Equations

Solving a System of Linear Equations
To solve a system of n linear equations with n variables, use an n-
element constant vector, an n x n coefficient matrix, and division ([IJ).
The constant vector contains the constant values of the equations. The
coefficient matrix contains the coefficients of the variables.
The next example shows how to solve a system of three linearly inde-
pendent equations in three variables. Suppose the equations are
3x + y + 2z 13
x + y 8z -1
- x + 2y + 5z 13
Enter the constant vector.
II] 13, -1 ,13 I ENTER I
Key in the coefficient matrix.
II] II] 3,1,2
II] 1,1,-8
II] -1,2,5
Solve the system of equations.
[IJ
3: 1
2: [ 68 85 85 ]
1: [ 13 -1 13 ]
t!!lBIem~lIIDIo::mJmIm
2: [ 68 85 85 ]
1: [ 13 -1 13 ]
[ [
3, 1 , 2 [1 , 1 , - 8 [ - 1 , 2, 50
t!!lBIem~lIIDIo::mJmIm
3: 1
2: [ 68 85 85 ]
1: [ 2 5 1 ]
t!!lBIem~lIIDIo::mJmIm
The values in the solution vector are the values of the variables that
satisfy the equations:
x = 2, Y = 5, Z = 1
To solve under-determined, over-determined, or near-singular sys-
tems of equations, refer to "ARRAY" in the Reference Manual.
130 11: Vectors and Matrices