HP 50g manual Solution of linear systems, Using the numerical solver for linear systems

Solution of linear systems

A system of n linear equations in m variables can be written as

a11⋅x1 + a12⋅x2 + a13⋅x3 + …+ a1,m-1⋅x m-1+ a1,m⋅x m = b1, a21⋅x1 + a22⋅x2 + a23⋅x3 + …+ a2,m-1⋅x m-1+ a2,m⋅x m = b2, a31⋅x1 + a32⋅x2 + a33⋅x3 + …+ a3,m-1⋅x m-1+ a3,m⋅x m = b3,

. . . … .. .

an-1,1⋅x1 + an-1,2⋅x2 + an-1,3⋅x3 + …+ an-1,m-1⋅xm-1 + an-1,m⋅xm = bn-1,an1⋅x1 + an2⋅x2 + an3⋅x3 + …+ an,m-1⋅xm-1+ an,m⋅x m = bn.

This system of linear equations can be written as a matrix equation, An⋅m⋅xm⋅1 = bn⋅1, if we define the following matrix and vectors:

⎡a11	a12	L a1m		⎤
⎢		L		⎥
A = ⎢a21	a22		a2m ⎥
⎢ M	M	O	M	⎥
⎢		L		⎥
⎣an1	an2		anm ⎦ n⋅m
				,

⎡⎢ x1 ⎤⎥ x = ⎢ x2 ⎥ ⎢ M ⎥ ⎢ ⎥

⎣xm ⎦ m⋅1 ,

⎡⎢b1 ⎤⎥ b = ⎢b2 ⎥ ⎢ M ⎥ ⎢ ⎥

⎣bn ⎦ n⋅1

Using the numerical solver for linear systems

There are many ways to solve a system of linear equations with the calculator. One possibility is through the numerical solver ‚Ï. From the numerical solver screen, shown below (left), select the option 4. Solve lin sys.., and press @@@OK@@@. The following input form will be provide (right):

To solve the linear system A⋅x = b, enter the matrix A, in the format

[[ a11, a12, … ], … [….]] in the A: field. Also, enter the vector b in the B:

field. When the X: field is highlighted, press @SOLVE. If a solution is

available, the solution vector x will be shown in the X: field. The solution is also copied to stack level 1. Some examples follow.

The system of linear equations

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