Matrix solutions to systems of linear equations, Matrix solutions to systems of linear ec|uations, Matrix solutions to systems – HP 48g Graphing Calculator User Manual
Page 178: Linear equations
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14
To conjugate each element of a complex matrix:
1. Enter the complex matrix onto the stack.
2.
Press
(MTH 1 (NXT 1
C M P L
fNXT
)
C u N J
to conjugate each
complex element of the matrix.
To extract a matrix of real parts from a complex matrix:
1. Enter the complex matrix onto the stack.
2 .
Pres.s
(MTH") fNXT
) C M P L R E
to return a matrix containing
just the real parts of each element of the original complex matrix.
To extract a matrix of imaginary parts from a complex matrix:
1. Enter the complex matrix onto the stack.
2. Press ( M T H I (MXT 1
C M P L I M
to return a matrix containing
just the imaginary parts of each element of the original complex
matrix.
Matrix Solutions to Systems
of
Linear
Equations
Systems of linear equations fall into three categories:
■ Over-determined systems.
These systems have more linearly
independent equations than independent variables. There is
no exact solution to over-determined systems, so the “best”
(least-squares) solution is sought.
B Uiider-deterinined systems.
These systems have more independent
variables than linearly independent equations. There are either no
solutions or an infinite number of solutions for under-determined
systems. If a solution exists, you want to find the solution with the
minimum Euclidean norm; otherwise, you want to find a minimum
norm least-squares solution.
B Exactly-determined systems.
These systems have an equal number
of independent variables and equations. Usually (but not always),
there is a single exact solution for exactly-determined systems. (See
“Ill-Conditioned and Singular Matrices” on page 14-16.)
14-14 Matrices and Linear Algebra