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{SECT 0 {EXCHG {PARA 204 "" 0 "" {TEXT 241 21 "Introduction to Maple" 
}}{PARA 205 "" 0 "" {TEXT 242 29 "Solving Systems of Equations " }
{TEXT 243 44 "by Bob Bradshaw, Ohlone College, Fremont, CA" }{TEXT 
244 1 "\n" }{TEXT 245 6 "\nMaple" }{TEXT 244 55 " can solve systems of
 equations through the use of the " }{TEXT 245 5 "solve" }{TEXT 244 
62 " command. First, enter the equations and then use the command " }
{TEXT 245 20 "\nsolve(\{eqn1, eqn2, " }{TEXT 244 4 "eqn3" }{TEXT 245 
15 "\}, \{variables\})" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 20 "eqn1:=3
*x+5*y+7*z=9;" }{MPLTEXT 1 0 22 "\neqn2:=11*x-y+15*z=17;" }{MPLTEXT 1 
0 19 "\neqn3:=x+y+23*z=25;" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 40 "ans
wer:=solve(\{eqn1,eqn2,eqn3\},\{x,y,z\});" }}}{EXCHG {PARA 205 "" 0 ""
 }{PARA 205 "" 0 "" {TEXT 244 51 "Unlike what you did in a beginning a
lgebra course, " }{TEXT 245 5 "Maple" }{TEXT 244 53 " can solve system
s with more equations than unknowns." }}{PARA 206 "> " 0 "" {MPLTEXT 
1 0 18 "eqn1:=3*x+y+7*z=9;" }{MPLTEXT 1 0 16 "\neqn2:=x-y+z=17;" }
{MPLTEXT 1 0 36 "\nanswer:=solve(\{eqn1,eqn2\},\{x,y,z\});" }}}{EXCHG 
{PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 245 5 "Maple" }{TEXT 244 
50 " can solve systems with non-constant coefficients." }}{PARA 206 ">
 " 0 "" {MPLTEXT 1 0 27 "eqn1:=a*x+b*sin(t)*y+z^2=9;" }{MPLTEXT 1 0 
18 "\neqn2:=3*x-5*y=17;" }{MPLTEXT 1 0 34 "\nanswer:=solve(\{eqn1,eqn2
\},\{x,y\});" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 
245 5 "Maple" }{TEXT 244 46 " can also solve systems with non-linear t
erms." }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 17 "eqn1:=x^2+y^2=25;" }
{MPLTEXT 1 0 13 "\neqn2:=x-y=1;" }{MPLTEXT 1 0 34 "\nanswer:=solve(\{e
qn1,eqn2\},\{x,y\});" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" 
{TEXT 244 40 "Often, when solving non-linear systems, " }{TEXT 245 5 "
Maple" }{TEXT 244 45 " may return the answer in an unreadable form." }
}{PARA 206 "> " 0 "" {MPLTEXT 1 0 20 "eqn1:=3*x^2+5*y^2=9;" }{MPLTEXT 
1 0 17 "\neqn2:=11*x-y=17;" }{MPLTEXT 1 0 34 "\nanswer:=solve(\{eqn1,e
qn2\},\{x,y\});" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 
244 6 "Using " }{TEXT 245 5 "evalf" }{TEXT 244 4 " or " }{TEXT 245 6 "
fsolve" }{TEXT 244 35 " will only give one of the answers." }}{PARA 
206 "> " 0 "" {MPLTEXT 1 0 14 "evalf(answer);" }{MPLTEXT 1 0 21 "\nfso
lve(\{eqn1,eqn2\});" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" 
{TEXT 244 6 "Using " }{TEXT 245 9 "allvalues" }{TEXT 244 41 " will giv
e both answers but in exact form" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 
109 "### WARNING: allvalues now returns a list of symbolic values inst
ead of a sequence of lists of numeric values" }{MPLTEXT 1 0 19 "\nallv
alues(answer);" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 
244 10 "Combining " }{TEXT 245 5 "evalf" }{TEXT 244 6 " with " }{TEXT 
245 9 "allvalues" }{TEXT 244 30 " will give all decimal values." }}
{PARA 206 "> " 0 "" {MPLTEXT 1 0 109 "### WARNING: allvalues now retur
ns a list of symbolic values instead of a sequence of lists of numeric
 values" }{MPLTEXT 1 0 26 "\nevalf(allvalues(answer));" }}}{EXCHG 
{PARA 205 "" 0 "" }{PARA 207 "" 0 "" {TEXT 246 14 "Linear Algebra" }}
{PARA 205 "" 0 "" {TEXT 244 12 "The package " }{TEXT 245 6 "linalg" }
{TEXT 244 66 " provides many new commands for dealing with systems of \+
equations." }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}
{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 244 12 "In general, \+
" }{TEXT 245 5 "Maple" }{TEXT 244 32 " describes a matrix as an array.
" }}{PARA 205 "" 0 "" {TEXT 244 1 " " }{TEXT 247 24 "A:=array([[2,3],[
4,5]]);" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 244 42 "
To multiply two matrices, use the command " }{TEXT 245 22 "evalm(matri
x * matrix)" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 11 "evalm(A*A);" }}}
{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 244 71 "You can find
 the determinant of a matrix using the determinant command " }{TEXT 
245 3 "det" }{TEXT 244 1 "." }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 7 "det
(A);" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 244 124 "In
 linear algebra and finite math, systems of linear equations are solve
d using a technique called Gauss-Jordan elimination." }}{PARA 205 "" 0
 "" {TEXT 244 25 "First, create a matrix A." }}{PARA 206 "> " 0 "" 
{MPLTEXT 1 0 43 "A:=array([[1,2,2,3],[-1,2,6,5],[1,2,3,2]]);" }}}
{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" {TEXT 244 34 "The matrix h
as three rows so tell " }{TEXT 245 5 "Maple" }{TEXT 244 47 " to do thr
ee steps of Gauss-Jordan elimination." }}{PARA 206 "> " 0 "" {MPLTEXT 
1 0 20 "for i from 1 to 3 do" }{MPLTEXT 1 0 15 "\ngaussjord(A,i)" }
{MPLTEXT 1 0 4 "\nod;" }}}{EXCHG {PARA 205 "" 0 "" }{PARA 205 "" 0 "" 
{TEXT 244 87 "Compare the matrix A and this final matrix to the system
 of equations and its solution." }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 
18 "eqn1:=x+2*y+2*z=3;" }{MPLTEXT 1 0 20 "\neqn2:=-x+2*y+6*z=5;" }
{MPLTEXT 1 0 19 "\neqn3:=x+2*y+3*z=2;" }{MPLTEXT 1 0 33 "\nsolve(\{eqn
1,eqn2,eqn3\},\{x,y,z\});" }}}{EXCHG {PARA 208 "" 0 "" }{PARA 209 "" 0
 "" {TEXT 248 11 "You Try It!" }}{PARA 205 "" 0 "" {TEXT 244 45 "1.  F
ind the solution to the set of equations" }}{PARA 205 "" 0 "" {TEXT 
244 1 "3" }{TEXT 245 1 "x" }{TEXT 244 4 " + 5" }{TEXT 245 1 "y" }
{TEXT 244 4 " + 2" }{TEXT 245 1 "z" }{TEXT 244 4 " - 3" }{TEXT 245 1 "
w" }{TEXT 244 4 " = 9" }}{PARA 205 "" 0 "" {TEXT 244 1 "4" }{TEXT 245 
1 "x" }{TEXT 244 4 " + 7" }{TEXT 245 1 "y" }{TEXT 244 4 " + 5" }{TEXT 
245 1 "z" }{TEXT 244 3 " - " }{TEXT 245 1 "w" }{TEXT 244 5 " = 19" }}
{PARA 205 "" 0 "" {TEXT 244 1 "3" }{TEXT 245 1 "x" }{TEXT 244 4 " + 6"
 }{TEXT 245 1 "y" }{TEXT 244 4 " + 2" }{TEXT 245 1 "z" }{TEXT 244 4 " \+
- 2" }{TEXT 245 1 "w" }{TEXT 244 4 " = 3" }}{PARA 205 "" 0 "" {TEXT 
245 1 "x" }{TEXT 244 4 " + 9" }{TEXT 245 1 "y" }{TEXT 244 4 " - 8" }
{TEXT 245 1 "z" }{TEXT 244 5 " - 13" }{TEXT 245 1 "w" }{TEXT 244 5 " =
 29" }}{PARA 205 "" 0 "" {TEXT 244 42 "2.  Sketch the graph of the two
 equations " }{XPPEDIT 18 0 "x^2+y^2 = 9;" "6#/,&*$%\"xG\"\"#\"\"\"*$%
\"yGF'F(\"\"*" }{TEXT 249 1 " " }{TEXT 244 5 " and " }{XPPEDIT 18 0 "x
^2/16+y^2 = 1;" "6#/,&*&%\"xG\"\"#\"#;!\"\"\"\"\"*$%\"yGF'F*F*" }
{TEXT 249 1 " " }{TEXT 244 6 ". Use " }{TEXT 245 5 "Maple" }{TEXT 244 
33 " to find the intersection points." }}{PARA 205 "" 0 "" {TEXT 244 
68 "3.  Use the method of Gauss-Jordan elimination to solve problem (1
)." }}{PARA 205 "" 0 "" }}{PARA 210 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }