Matrices 15-15 | HP 39gs Graphing specs

The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions.

Matrices

15-15

Image 203

HP 39gs Graphing manual Matrices 15-15

Contents

Edition3 Part Number F2223AA-90001 Users guide Edition December June Printing HistoryUSA Contents 10-6 Using variables in equations10-1 11-9 11-111-4 11-8 14-4 13-24Program constants 13-24 Physical constants 13-25 Introduction 14-1 Storing and recalling variables 14-2 19-1 18-718-9 18-30 Service Regulatory information Function, Polar, Parametric PrefaceManual conventions Hewlett Packard’s Calculators web site can be found atPage Home On/off, cancel operationsGetting started Contrast To adjustDisplay Parts of the display Infrared or cable KeyboardMenu keys Aplet views on Aplet control keysAplet library on Displays the Views menu. See Button performs Entry/Edit keys Shifted keystrokes Math keys Helpwith Inactive keys CommandsMenus Program Input forms Reset input form values You use the Modes input form to set the modes for Home Mode settings Setting a mode Press to return to Home Aplets E-lessons Another sequence, such as Un 1 Example x = cost and y = sintPolar Sequence Sequence functions U in terms of n, or Quad Explorer aplet Transformations reflected in the equation Aplet views Symbolic view Plot viewPress to display the aplet’s Symbolic view Aplet library Select Overlay Plot Select Plot-TableSelect Plot-Detail Sketch view Aplet view configurationPlot Setup Numeric Setup Symbolic Setup Entering expressions Where to startTo save aplet configuration Mathematical calculations 23 3 EEX Long results Negative numbers Scientific notation powersUsing Explicit and implicit multiplication Entering Calculates Sin 45 + π Parentheses Input Output Last input Edit line Last output Getting started Storing a value in a variable Setting Fraction mode Using fractionsAccessing the display history Clearing the display history Setting fraction precision Fraction Fraction calculationsSelect Fraction as Converting decimals to fractionsEnter the calculation Evaluate the calculation This example, the fraction precision is set to Complex numbers Catalogs and editors Aplet views About the Symbolic viewDefining an expression Symbolic view Aplets and their views Independent variable in the expressions is T Select Function Evaluating expressionsAplets Home About the Plot view Setting up the plot Plot view setup ΘSTEP Plot view settingsΘRNG Exploring the graph Reset plot settings To move between relations Trace a graph Zoom options Zoom within a graphTo jump directly to a value To turn trace on/off Auto Scale SquareSet Factors Now un-zoom Un-zoom To box zoom Views menu options Other views for scaling and splitting the graph Pixel=π/24 radian, 7.58, or Unit. Resets default values forSplit the screen Making each pixel=1 unit. Not Trigonometric Overlay plotsDecimal scaling Integer scaling About the numeric view Setting up the table Numeric view setup NUM view menu keys Zoom within a table Numeric view settingsExploring the table of numbers Integer Numstart and Numstep Numtype Build Your Own Building your own table of numbersBuild a table Clear data Example plotting a circle Build Your Own menu keys Display the functions in numeric form Reset the graph setup to the default settingsFunction aplet, specify the functions FunctionPage Open the Function aplet Function apletAbout the Function aplet Getting started with the Function aplet Plot the functions Define the expressions Set up the plotPlot the functions Specify a grid for the graph Times Change the scale Trace a graphSelect Auto Scale Select Root Analyse graph with FCN functions Select Signed area Select Slope Select Extremum To find the extremum of the quadratic Display the table of values Display the numeric viewExplore the table To display Symbolic definition A columnDisplay the symbolic definition for the F1 column Symbolic definition F1 is displayed at Bottom of the screen Or to choose a variable Function aplet interactive analysisSelect Plot FCN Slope FCN functionsRoot Extremum Cursor. You need to have at Symbolic view. DisplaysShading area Intersection Plotting a piecewise-defined function Define the expressions Parametric apletAbout the Parametric aplet Getting started with the Parametric aplet Select Degrees Set up the plot Plot the expressionSet angle measure Set the angle measure to degrees 120 Overlay plot Display the numbersPlot a triangle graph over the existing circle graph Page Select Polar Polar apletGetting started with the Polar aplet Open the Polar aplet Display the Plot view menu key labels Explore the graph Display the numbers Getting started with the Sequence aplet Sequence apletAbout the Sequence aplet Menu keys to assist in the entry of equations Define the expression Specify plot settingsOpen the Sequence aplet Sequence Display the . Display the table of values for this example Plot Setup, set the Seqplot option to CobwebPlot the sequence Select CobwebPage About the Solve aplet Solve aplet Select Solve Getting started with the Solve apletOpen the Solve aplet Define the equation Enter known variables Modes is set to Comma, use instead Solve the unknown variable Plot the equation Displays other pages of variables, if Plot the equation for variable aSolve aplet’s NUM view keys are Copies the highlighted value to Use an initial guess Interpreting results Consider the equation of motion for an accelerating body Plotting to find guesses Plot the graph To highlight T Press until the cursor is at the intersection Using variables in equations Solver Linear Solver apletOpen the Linear Sequence aplet Select Linear Hence we need the three-equation input form Solver was able to find solutions for x, y, and z as Linear Solver aplet Page About the Triangle Solver aplet Triangle Solve aplet Triangle Solver Open the Triangle Solver aplet Errors Addition, you cannot specify only angles and no lengths Not enough data Getting started with the Statistics aplet Statistics apletAbout the Statistics aplet To move to the next column Enter dataSelect Statistics Enter the data into the columns Value is Select a fit in the Symbolic setup viewChoose fit and data columns Explore statistics Slope m is 425.875. The y-intercept b is Setup plot Plot the graph Draw the regression curveDisplay the equation for best linear fit To move to the FIT1 field Stat-Two Predict valuesTo highlight Statistics aplet’s Numeric view keys are Entering and editing statistical data Statistics Expression Expression in standard Mathematical form. Press When DoneCopies the column variable or Variable expression to the edit line Again before re-use Clear is usedData sets will need to be selected Plot a histogram of the data Save data Edit a data set Sort data values Delete data Insert data Fit models Angle SettingDefining a regression model To choose the fit To define your own fit 7,8,15,16,17 Computed statistics Columns for a linear fit only PlottingTwo-variable To plot statistical data Plot typesHistogram Box and Whisker Plot Correlation coefficient Fitting a curve to 2VAR dataScatter Plot Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup viewRelative Error Erases the plot Trouble-shooting a plotStatistics aplet’s Plot view keys Model Calculating predicted valuesFind predicted values According to the current regression Statistics aplet 10-21 Page Open the Inference aplet Inference apletAbout the Inference aplet Getting started with the Inference aplet Inference aplet’s Symb view keys Table below summarizes the options available Symbolic view Test 1 μ Setup-NUMSelect the inferential method Enter data Select Hypoth Test Importing sample statistics from the Statistics aplet Are explained in the feature of this aplet Produced by the calculator 529 295 952 259 925 592 If the Decimal Mark setting in the Modes input formStatistics aplet opens in the Numeric view C1 column, enter the random numbers Select Conf Interval Set up the interval calculationOpen Inference aplet Inference To move to the C field Display Numeric view Display Plot viewSpecify a 90% Confidence interval in the C field Inputs Hypothesis testsOne-Sample Z-Test Menu name Results Two-Sample Z-Test Measures the strength of the evidence for a selected One-Proportion Z-TestPopulation 2 standard Test 1π Two-Proportion Z-Test One-Sample T-Test With the α level that you Sample standard deviation Pooled? Two-Sample T-Test One-Sample Z-Interval Confidence intervals Two-Sample Z-Interval Two-Proportion Z-Interval One-Proportion Z-Interval One-Sample T-Interval Pooled Two-Sample T-Interval Critical T Critical value for T Background Using the Finance Solver 3 4 Compounding period -- which is PMT Performing TVM calculations Example 1 Loan calculations Example 2 Mortgage with balloon payment To continue amortizing the loan Calculating AmortizationsTo calculate amortizations Example 3 Amortization for home mortgage Example 4 Amortization for home mortgage Name. Note You do not need to press first Using mathematical functionsMath functions Math menu Functions common to keyboard and menus Math functions by categoryFunction categories Syntax E5 returns Keyboard functionsValue1+ value2 , etc Evalue LOG100 returns Returns ABS1,2 returns S1,2*X+3,X Calculus functionsNthroot 8 returns ∂ s1s1 2+3*s1 returns 2*s1+3 Conj Complex number functionsTaylor ARG Minreal ConstantsConversions Maxreal Hyperbolic trigonometry Loop functions List functions Polyeval Matrix functionsPolynomial functions Polycoef Perm Probability functionsPolyroot Comb Real-number functions Frac DEG→RADFloor Fnroot MIN INTMant MAX Sign TotalRAD→DEG Round Isolate Symbolic functionsTwo-variable statistics Xpon QUADX-12-7,X returns Test functionsQuad Quote XOR Trigonometry functionsIfte Not Symbolic calculations To find derivatives in Home Finding derivatives Select F2X and evaluate it To find derivatives in the Function aplet’s Symbolic viewEvaluate the function Show the result For example, to find the indefinite integral To find the indefinite integral using formal variablesYou could also just define Program constants Program constants and physical constants Physical constants 13-26 Introduction Variables and memory management Storing and recalling variables To clear a variable To use variablesCalculations Press Vars menuOpen the Vars menu Result in another list variable Add the contents of two list variables, and to storeNames or values of variables into programs Example 14-6 17-5 for more information on That you can configure usingTo store into a graphics variable on Aplet variables on page R-7 To access an apletX0, Y0 to X9, Y9 Symbolic view. See Variable To delete variables in a category Memory ManagerLine, press and press Details of variables within the categoryPage Matrix Variables MatricesVectors Matrices POLYROOT1,0,-1,0 M1 Creating and storing matricesMatrix Catalog keys To create a matrix in the Matrix Catalog To transmit a matrix Working with matrices Moves to the first row, last row, first Deletes the highlighted cells, rowOr column you are prompted to Make a choice Create the second matrix Matrix arithmeticTo store one element Matrices 15-7 Open the Matrix catalog and create a vector Solving systems of linear equations Select Real matrix About functions Matrix functions and commandsAbout commands Argument conventions DOT CondCross DET Rref MakematRank Rownorm Examples Transposing a Matrix Reduced-Row Echelon Form Matrices 15-15 Page You can create, edit, delete, send, and receive named Lists List catalog keys List edit keys Create a list Element Displaying and editing listsTo display a list To display one 148 L12 A listTo insert an element 1. Open the List catalog Press , and press To delete a list List functionsDeleting lists Transmitting lists ΔLISTlist1 2,3 returns 5,10,15CONCATlist1,list2 CONCAT1,2,3,4 returns 1,2,3,4 ΠLIST2,3,4 returns 23 27 Calculates the product of all elements in listΠLISTlist Finding statistical values for list elements 16-10 Or to exit the Notes view Aplet note viewTo write a note in Note view Your work is automatically saved. Press any view key Alpha-lock for letter entry Contents of variablesCommands Space key for text entry To draw a line Aplet sketch viewSketch keys Draw keys To draw a box Press to continue drawing, or press Mynote Another HP 39gs or PC Opens the selected note forBegins a new note, and asks For a name Press instead Programming Contents of a Program Structured Programming Programs that perform smaller tasks Program catalogOpen Program Catalog Be simple-or it can be divided further into other Program catalog keys Press Progrm to open the Program catalog Creating and editing programsCreate a new program Edit a program 1. Press Progrm to On the left, use or to highlight a commandPress to paste the command into the program editor Editing keys Run a program Debug a program Stop a program Using programs Transmit a program Customizing an aplet Example Aplet naming convention Save the aplet Configuring the Setviews menu option programs ’’ ’’’’EXP.SV’’0 Setviews ’’’’ ’’’’18’’My Entry1’’’’EXP.ME1’’1 ’’My Entry2’’’’EXP.ME2’’3 ’’Start’’’’EXP.S’’7 Programming commands’’’’’’EXP.ANG’’0 Setviews Aplet commandsCheck Select Auto-run programs Associating programs with your aplet Including standard menu options ProgramNameViewNumber Uncheck n Branch commandsUncheck IF...THEN...END If A==1 IF... THEN... ElseEND CASE...END Iferr Then ELSE… END Stop Drawing commandsRUN Line BOXErase Freeze Graphic commands →PLOT GrobxorMakegrob PLOT→ Loop commands Matrix commands Scaleadd RandmatRedim Scale Prompt commands Print commands Disp 3A is 2+2 ClrvarDisp Dispxy Editmat matrixname Disptime51.52HELLO Msgbox GetkeyInput Stat-Two commands Stat-One and Stat-Two commandsStat-One commands Storing and retrieving variables in programs Plot-view variables InvCross GridHmin/Hmax Indep Root IsectLabels Recenter Slope S1mark-S5markSeqPlot Simult Tracing Umin/UmaxUstep Tmin / Tmax Ytick TstepXcross Ycross Yzoom Ymin / Ymax Symbolic-view variables Cubic S2fit S1fit...S5fit Format Numeric-view variablesC1...C9, C0 Digits NumRow NumColNumFont NumIndep StatMode NumStepNumType NumZoom Graphicname Sketch variablesPageNum Following aplet variable is available in Note view Creating new aplets based on existing aplets Extending aplets Degrees Open the Solve aplet and save it under the new nameSolve Choose the sine formula in E1 Resetting an apletUsing a customized aplet Hewlett-Packard’s Calculators web site can be found at Downloading e-lessons from the webSending and receiving aplets To transmit an aplet To sort the aplet list To delete an aplet Sorting items in the aplet library menu list Cross matrix1,matrix2 Reference informationGlossary Expression line# Set to Comma and enclosed Editor and catalog Matrix Two-dimensional array of valuesRecord using the Program editor Vector One-dimensional array of values To reset using the keyboard Resetting the HP 39gsTo erase all memory and reset defaults Batteries Operating detailsIf the calculator does not turn on To install the main batteries To install the backup battery Home variables Variables Angle Function aplet variablesArea Root Extremum Slope Isect Parametric aplet variables are Category Available name Plot Parametric aplet variables Polar aplet variables are Category Available names Plot Polar aplet variables Sequence aplet variables are Category Available name Plot Sequence aplet variables Digits NumCol Format NumRow Solve aplet variablesSolve aplet variables are Category Available name Plot Statistics aplet variables Hyperb Math menu categoriesMath functions Math functions are Category Available name Calculus Polynom Category Available name Matrix Stat1Var Stat2Var Degrees Grads RadiansStandard Sci Fixed Eng Fraction Cobweb Stairstep Wavelength, λc Compt w... Compton Print Program commandsProgram commands are Category Command Aplet Branch Status messages Category Command Stat-Two Function value, root, extremum Also be correct. Look upFunction name in the index to Find its proper syntaxPage HP 39gs Graphing Calculator Warranty period 12 months Limited WarrantyPage Service Rotc = Rest of the country Canada 905 206-4663 or Regulatory information This marking is valid for EU XxxxPage Page Branch structures 18-17 build your own table Index Contrast Freeze 18-20 Line 18-20 Pixoff 18-20 Pixon 18-20 Tline Acosh Alog Asinh Atanh Cosh EXP GroborPage Page Angle measure 1-10 decimal mark 1-11 number format Trigonometric scaling 2-14 two-variablestatistics Sending and receiving 18-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Page