Hp 38g Graphing Calculator Manuel d'utilisateur télécharger pdf (Page 138)

Solving Systems of Linear Equations

Remember that a system of equations can be represented by

a matrix equation :

Equation Form Matrix Form

ax + by + cz =

dx + ey + fz = kj^

gx + hy + iz =

c X

f y

h i

Using the matrix form, the solution is the vector of variables,

as shown below.

Constants

Vector

[^1» ^2*^3]

Coefficients Matrix Variables

Vector (result)

[[a,b.c]{d.e,f\[S,h.i]] [x, y. z]

The coefficient matrix must be square (the number of

coefficients per equation equals the number of equations).

To solve linear 1. tn Home, enter the constants vector or the name of a

equations

Example

stored constants vector (Ml ...M9, MO). (This must be a

vector, which has a single set of brackets, not a matrix,

which has multiple sets of brackets.)

2. Press [7].

3. Enter the coefficients matrix or the name of a stored

square coefficients matrix (Ml ...M9, MO).

4. Press [enter] . The resulting variables vector is displayed.

Find all [x, y, z] satisfying

2x + 3y + 4z = 6

X + y - z = 0

4x - y + 2z = 6

The constants vector is [6,0,6]. The coefficients matrix is

[[2,3,4],[1,1,-1],[4, -1,2]]. The solution for this system of

linear equations (that is, constants vector divided by

coefficients matrix) is [1,0,1].

6-8 Using Matrices

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Hp 38g Graphing Calculator Manuel d'utilisateur Page 138