Manuals / HP / Computer Equipment / Calculator

HP 40G manual Solving systems of linear equations, +,7@MATRIX1 175@, 175@7 175@

Models: 40G

1 288

Page 180

Solving systems of linear equations

Example	Solve the following linear system:
	2x + 3y + 4z	= 5
	x + y – z	=	7
	4x – y +2 z	=	1

1.Open the Matrix catalog and choose to create a vector in the M1 variable.

>6+,)7@MATRIX1(:_

*e,>(17(5@

2.Create the vector of the constants in the linear system.

5 >(17(5@7 >(17(5@

1 >(17(5@

3.Return to the Matrix catalog. The vector you created is listed as M1.

>6+,)7@MATRIX

4.Select the M2 variable and create a new matrix.

*e,1(:_

Select2. Real matrix

5.Create a new matrix and enter the equation coefficients.

2 >(17(5@3 >(17(5@

4 >(17(5@*e,

1>(17(5@1 >(17(5@

>@1 >(17(5@ 4 >(17(5@ >@1>(17(5@ 2>(17(5@

12-8

Matrices

Page 180

Image 180

HP 40G manual Solving systems of linear equations, +,7@MATRIX1 175@, 175@7 175@, 175@3 175@ 175@*e 1175@1 175@

Contents

USER’S Guide Page Contents Parametric aplet Inference aplet Importing Sample Statistics from the Statistics apletVariables and memory management Programming Index Preface Manual conventions@, &26@, +20@, etc +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etcPreface On/off, cancel operations Getting startedHome To adjust the contrast To clear the display DisplayParts of the display Keyboard Menu keysAnnunciator Description Aplet control keys Key Meaning+,7@ $/3+$@175@ 75@Shifted keystrokes HelpwithKey Description +,7@$/3+$@Program commands Inactive keys Math keysTo cancel a menu MenusTo search a menu Mode settings Reset input form valuesSetting Options Input formsSetting Options Setting a mode Aplets E-lessonsPress+20@ to return to Home Aplet Use this aplet to explore Name Quad Explorer aplet N TTrig Explorer aplet *,*A, keysSymbolic view Plot view Numeric view Aplet libraryAplet views Aplets are stored in the Aplet libraryViews menu contains the Plot-Table view Aplet view configuration Plot Setup Numeric Setup SymbolicConfiguration To change viewsMathematical calculations Entering expressionsLong results Negative numbers ExampleScientific notation powers Explicit and implicit multiplication@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ Entering Calculates @ 45 @6+,7@π+,7@√ 85@9 +,7@√ @85 @9 @Clearing numbers Using previous results 175@ updates ANS from 50 to 75 to 50175@ @25 175@175@Accessing the display history $/3+$@ a 175@Key Function Using fractions Setting Fraction modeSee Setting fraction precision below for more information Clearing the display historySetting fraction precision Fraction calculations Converting decimals to fractions Return to Home and enter the calculation@@@2@3 Evaluate the calculationComplex numbers Converting a number to a fractionComplex results To enter complex numbers + iyCatalog/Editor Contents Catalogs and editorsStoring complex numbers Differences between the HP 38G and the HP 39G/40G Memory manager Plot Goto functionStatistics Pred function Trig Explorer and Quadratic Explorer apletsPage About the Symbolic view Defining an expression Symbolic viewAplets and their views Aplet viewsAplets and their views Evaluating expressions ApletsHome Symb view keys $56@$7+@ +,7@CLEARSetting up the plot Plot view setup Plot view settingsAbout the Plot view 175@ orReset plot settings Exploring the graph Plot view keys+,7@*A Trace a graph Zoom within a graphTo jump directly to a value To turn trace on/ off Zoom optionsDivides horizontal scale only, using Multiplies horizontal scale, usingDivides vertical scale only, using Multiplies vertical scale only, using018Zoom =220Un-zoomPress *k, to move to the bottom of the Zoom list =220Zoom Out=220X-Zoom =220X-Zoom Out=220Y-Zoom =220Y-Zoom OutTo box zoom To set zoom factors Other views for scaling and splitting the graph OptionsMenu key copies the right plot to the left About the numeric view Overlay plotsDecimal scaling Integer scaling Trigonometric scalingSetting up the table numeric view setup Numeric view settingsReset numeric settings Exploring the table of numbers NUM view menu keysZoom within a table Building your own table of numbers Arrow keys to place the cursor in the independent variableColumn, then enter the value to jump to 175@, the values for the dependent variables areBuild Your Own menu keys Clear dataExample plotting a circle $3/7@ Select+,7@√@9 Function aplet About the Function apletGetting started with the Function aplet Open the Function apletDefine the expressions Plot the functions@75@175@ Plot the functionsChange the scale Trace a graph With FCN functionsTrace the linear function TimesFind the greater of the two roots of the quadratic function SelectRootRoot value is displayed at the bottom of the screen 2Select.Slope Move the cursor to x = 1 by pressing the *A,orChoose the end value for @.2Display the numeric view Set up the table Display the numeric setupTo find the extremum of the quadratic Display the numeric viewMatch the table settings to the pixel columns in the graph Explore the tableDisplay a table of numeric values Move to X =Function aplet interactive analysis Area Extremum Isect Root SlopeAccess FCN variables FCN functions Function DescriptionSymbolic view. Displays Cursor. You need to have at leastTwo selected expressions Plotting a piecewise defined function example = $3/ @ Select Page Parametric aplet About the Parametric apletGetting started with the Parametric aplet Open the Parametric aplet Define the expressionsSet angle measure Set up the plot Plot the expression +,7@PLOT360 Overlay plot Display the numbers Plot a triangle graph over the existing circle graph+,7@ Plot 120Page Polar aplet Getting started with the polar apletOpen the Polar aplet +,7@CLEAR 46+,7@π 2.aExplore the graph Display the numbers Sequence aplet starts in the Symbolic view Sequence apletAbout the Sequence aplet Getting started with the Sequence apletDefine the expression Keys to assist in the entry of equationsPlot Setup, set the Seqplot option to Cobweb Plot the sequence Display the tablePlot the Fibonacci sequence Select CobwebPage Solve aplet About the Solve apletGetting started with the Solve aplet Open the Solve apletDefine the equation Define known variables Solve the unknown variable Plot the equation Solve for the unknown variable a@ Select Auto Solve aplet’s NUM view keys ≈20 timesUse an initial guess Number formatInterpreting results Message ConditionRoot- Finder at work Plotting to find guesses At2 x = v0t +$/3+$@X 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight TPlot the graph To move cursor to the intersectionUsing variables in equations Home variablesInitial guess 3175@*k,*k,*kStatistics aplet About the Statistics apletGetting started with the Statistics aplet 1400 920 1100 2265 2890 2200Open the Statistics aplet Enter data 175@1 175@ 175@5 175@ 175@4 175@To move to the next column 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@Choose fit and data columns Explore statistics Setup plot Select a fit in the Symbolic setup viewSelect2. Linear Display the equation for the best linear fit To move to the FIT1 +2fieldEntering and editing statistical data $7+@ S to highlightTo highlight 6175@Statistics aplet’s NUM view keys +,7@ FXUVRU160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Sets will need to be selected again Before re-useHeight cm Frequency Angle Setting Save dataDelete data Defining a regression model 2VAR Insert data Sort data valuesTo choose the fit Select the Sort Order option. You can choose eitherFit models To define your own fit Fit model Meaning= m lnx + b = ax3+bx2+cx+d. Needs at leastComputed statistics One-variableStatistic Definition Two-variable Columns for a linear fit onlyPlotting To plot statistical dataYou can plot Plot types Histogram Box and Whisker Plot Scatter PlotRelative Error Fitting a curve to0182VAR dataCorrelation CoefficientSetting up the plot Plot setup view Plotting mark 2VAR Connected points 2VARTrouble-shooting a plot Statistics aplet’s Plot view keys Calculating predicted values Find predicted valuesPage Default the input form contains example data. This example Inference apletAbout the Inference aplet Example dataGetting started with the Inference aplet Open the Inference apletInference aplet’s Symb view keys Hypothesis Tests Confidence IntervalsDefine the inferential method ∝.a∝Field name Definition Open Statistics aplet. Note Reset current settings Importing Sample Statistics from the Statistics apletPlot test results Open the Statistics apletCalculate statistics Open Inference aplet @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@Choose inference method and type Import the data2one.a Display Numeric view Display Plot view Specify a 90% confidence interval in the C fieldE, to move to Field Display the confidence interval in the Plot viewHypothesis tests One-Sample Z-TestMenu name InputsTwo-Sample Z-Test ResultsResult Description One-Proportion Z-Test Two-Proportion Z-Test Successes in the two populations is equalH0 π1 = π2 One-Sample T-Test Test 1 ∝Selected hypothesis against the null hypothesis. The null Hypothesis is that the sample mean has some assumed valueTwo-Sample T-Test Sample 1 standard deviation Sample 2 standard deviationConfidence intervals Confidence interval calculations that the HP 39G/40G canPerform are based on the Normal Z-distribution or Student’s Confidence levelTwo populations, ∝1 ∝2, when the population standard Two-Sample Z-IntervalConfidence interval for the difference between the means Deviations, σ1 and σ2, are knownOne-Proportion Z-Interval Sample success countTwo-Proportion Z-Interval Successes in two populationsSample 1 success count Sample 2 success countOne-Sample T-Interval Two-Sample T-Interval Page Using mathematical functions Math functionsMath menu To select a function Function categoriesCalculus Loop Stat-Two Complex Matrices Math functions by category SyntaxFunctions common to keyboard and menus Keyboard functions +,7@ASIN +,7@ACOS+,7@ATAN +,7@√Valuepower +,7@ABSABSvalue +,7@ nCalculus functions TaylorVariableexpression Lower,upper,expression,variableComplex number functions ARGConj Constants Hyperbolic trigonometryList functions AlogEXP EXPM1Loop functions Matrix functionsIterate RecursePolynomial functions PolycoefPolyeval PolyformProbability functions CombPerm RandomUtpc UtpfUtpn UtptReal-number functions HMS→ →HMSINT MantMOD ChangeTotal RAD→DEGStatistics-Two SignTruncate XponSymbolic functions IsolateLINEAR? QuadQuote Trigonometry functions Symbolic calculations Symbolic calculations in the Function apletUsing formal variables HomeFinding derivatives To find derivativesGG@$/3+$@S1 Evaluate the functionTo find derivatives in the Function aplet’s Symbolic view GG@@$/3+$@To find the indefinite integral using formal variables +,7@GG@0 @ $/3+$@ S1 @ 3 @Show the result format Thus, substituting X for S1, it can be seen that10-26 Variables and memory management IntroductionStoring and recalling variables Numeric PrecisionTo store a value To store the results of a calculation Vars menu To use variablesCalculations 65 @$/3+$@A 175@Names or values of variables into programs +,7@LIST2contents,.a is copied to the command line $56@ *e,*e,*e,*A$/3+$@L3175@ List names directly from the keyboardCategory Available names To access an aplet variable Aplet variablesTo copy the value of the variable into the edit line Memory Manager Start the Memory Manager. a list of variable categoriesIs displayed +,7@MEMORYPage Matrices VectorsMatrices Matrix VariablesCreating and storing matrices Matrix Catalog keys+ 7@CLEAR +,7@*e, orTo create a matrix in the matrix catalog Select the type of matrix to createWorking with matrices To transmit a matrixClears all elements from the matrix +,7@*k, *e728 672? Matrix arithmetic To multiply and divide by a scalar175@ 2175@*e 175@ 4175@ 175@ 8 175@$/3+$@M1@ $/3+$@M2 175@ $/3+$@M1 j@$/3+$@M2 175@Solving systems of linear equations +,7@MATRIX1 175@175@7 175@ +,7@MATRIXMatrix functions and commands About functionsArgument conventions Eigenval EigenvvIdenmat InverseRank RownormRref SchurExamples TraceTRN Identity Matrix Transposing a MatrixReduced-Row Echelon Form Lists Creating listsCreate a list in the List Catalog Open the List catalogList catalog keys Create a list List edit keysDisplaying and editing lists To display a listTo display one element To edit a list @ /@16a*e To insert an element in a list To store one elementDeleting lists Transmitting listsTo delete a list To delete all listsList functions $/3+$@L 5175@ $7+@L *A $/3+$@L5175@$7+@L *A,Select $/3+$@A @Calculates the product of all elements in list POSlist, elementCalculates the number of elements in a list Sorts elements in ascending orderFinding statistical values for list elements 89@65@ 0@89$/3+$@ L1 175@ 180@67$76a Go to the Numeric view To display calculated statisticsPage Aplet note view To write a note in Note view+,7@letter Your work is automatically saved. Press any view key+,7@%.63$= +,7@ CmdsAplet sketch view Sketch keysTo draw a line Where you want any corner of the box to be You can adjust the size of the box by moving the cursorTo draw a box Draw keysKeys Press 2.again to affix the labelHighlight2. the variable name you want to use and press To import a graphics variable To create a note+,7@NOTEPAD Name of the note is ‘MYNOTE’Opens the selected note for Begins a new note, and asks forTransmits the selected note to Another HP 39G/40G or PC14-8 Contents of a Program Structured Programming ProgrammingProgram catalog Open Program catalogProgram catalog keys +,7@*k, or *eCreating and editing programs Create a new programEnter commands Edit a program +,7@CMDSA,*e To enter functions more to comeEditing keys Using programs Debug a program Stop a programRun a program From HOME, type RUN programname. or Working with programs Copy aProgram Transmit a program Delete a programDelete the contents of a program About customizing an apletDelete all ProgramsAplet naming convention Customizing an aplet example$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Programming commands Aplet commandsCheck SelectCommand syntax Syntax for the command is as followsAuto-run programs Branch commands UncheckIF...THEN...END If test-clauseIferr trap-clause Then error-clause END IF... thenELSE... END CASE...END Iferr Then ENDDrawing commands Graphic commands →GROB GrobnotGrobor GrobxorLoop commands Matrix commands Randmat RedimScale ScaleaddPrint commands Prompt commandsDisp DisptimeDisp linenumbertextitem Editmat matrixnameInput nametitle,labelhelpdefault GetkeyInput Msgbox PromptWait Wait secondsStat-One and Stat-Two commands Stat-One commandsStat-Two commands Storing and retrieving variables in programs Plot-view variablesArea AxesCoord ExtremumFastRes GridHwidth IndepInvCross IsectNmin / Nmax RecenterRoot S1mark-S5markSimult SlopeStatPlot Umin/UmaxTmin / Tmax TracingTstep XcrossXtick YtickXmin / Xmax Ymin / YmaxSymbolic-view variables XzoomYzoom AngleX1, Y1...X9,Y9 X0,Y0 R1...R9, R0U1...U9, U0 E1...E9, E0Numeric-view variables C1...C9, C0Digits Format NumColNumFont NumIndepNumRow NumStartNumStep NumTypePageNum Extending aplets Creating new aplets based on existing apletsAplet Keys $/3+$@ H 175@ $1@ $/3+$@ θ @$/3+$@ C @ 175@ $3/ @Select 180@ 35 175@Resetting an aplet Downloading e-lessons from the webSolve for the missing Length of the ladder is approximately 8.72 metresSending and receiving aplets To transmit an apletSorting items in the aplet library menu list To sort the aplet listTo delete an aplet Reference information Regulatory informationCanada LED safety WarrantyReference information Resetting the HP 39G/40G To reset using the keyboardTo erase all memory and reset defaults If the calculator does not turn on21@ key Glossary Cross matrix1,matrix2Operating temperature 0 to 45C 32 to 113F Operating detailsBatteries Menu maps of the Vars menu Home variables areCategory Available name Function aplet variables User-namedModes Function aplet variables areParametric aplet variables Plot-FCNParametric aplet variables are Polar aplet variables Polar aplet variables areSequence aplet variables Sequence aplet variables areSolve aplet variables Solve aplet variables areStatistics aplet variables Statistics aplet variables areStat-One Menu maps of the Math menu Math functionsMath functions are CalculusPolynom = =Program constants Program commands Category CommandSelected status messages Message Meaning+,7@ Memory Function value, root, extremum Or intersection is not visibleCurrent screen Index Index Index Index Index Index Index Index Index Index Index Index Index