HP 50g HP 50g_user's manual_English_HDPSG49AEM8.pdf - Page 122

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⋅x m-1 + an-1,m⋅x m = bn-1, an1⋅x1 + an2⋅x2 + an3⋅x3 + ...+ an,m-1⋅x m-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 ⎤ ⎡ x1 ⎤ ⎡b1 ⎤ A = ⎢⎢a21 ⎢M a22 M L O a2m ⎥ ⎥ M⎥ x = ⎢ ⎢ ⎢ x2 M ⎥ ⎥ ⎥ b = ⎢⎢b2 ⎢M ⎥ ⎥ ⎥ ⎢⎣an1 an2 L anm ⎥ ⎦ n×m , ⎢ ⎣ xm ⎥ ⎦ m×1 , ⎢⎣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 Page 9-9