HP 33s Scientific manual Solutions of Simultaneous Equations, 15-12Mathematics Programs

125 g @

)

63 g @ )

XD/ )

g/

)

g@

)

Sets T equal to 125.

Sets P equal to 63.

Calculates dot product.

Calculates angle between resultant force vector and lever. Gets back to input routine.

Solutions of Simultaneous Equations

This program solves simultaneous linear equations in two or three unknowns. It does this through matrix inversion and matrix multiplication.

A system of three linear equations

AX + DY + GZ = J

BX + EY + HZ = K

CX + FY + IZ = L

can be represented by the matrix equation below.

♠ A D G ≡ ♠ X ≡				♠ J ≡
↔ B E H	≈ ↔Y	≈	=	↔K	≈
↔	≈ ↔	≈		↔	≈
←C F I	… ← Z …			← L	…
↔	≈ ↔	≈		↔	≈

The matrix equation may be solved for X, Y, and Z by multiplying the result matrix by the inverse of the coefficient matrix.

♠ A ′			D ′
↔	B	′	E ′
↔
↔		′	F	′
←C

G H

I′

′≡ ♠ J

′≈≈ ↔↔K

≈ ↔ L … ←

≡		♠ X ≡
≈	=	↔Y	≈
≈		↔	≈
≈		↔	≈
…		← Z …

Specifics regarding the inversion process are given in the comments for the inversion routine, I.

15–12Mathematics Programs