Multiplication, RPN mode, try the following eight examples | HP 49g

In RPN mode, try the following eight examples:

22	2	2	2
A33	2	2	2

`B33`+A33`B33`-

Multiplication

There are different multiplication operations that involve matrices. These are described next. The examples are shown in algebraic mode.

Multiplication by a scalar

Some examples of multiplication of a matrix by a scalar are shown below.

Matrix-vector multiplication

Matrix-vector multiplication is possible only if the number of columns of the matrix is equal to the length of the vector. couple of examples of matrix- vector multiplication follow:

Vector-matrix multiplication, on the other hand, is not defined. This multiplication can be performed, however, as a special case of matrix multiplication as defined next.

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HP 49g manual Multiplication, RPN mode, try the following eight examples

Contents

Graphing calculator User’s manualPage Preface Page Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Calculus Applications GraphicsMulti-variate Calculus Applications Vector Analysis Applications Probability Distributions Differential EquationsStatistical Applications Service, W-2 Regulatory information, W-4 Limited Warranty W-1Numbers in Different Bases Basic Operations Chapter Getting startedBatteries Contents of the calculator’s display Tool menu MenusAssociated with the six soft menu keys, F1 through F6 Introducing the calculator’s keyboard Setting time and datePage Alpha function, to enter the upper-case letter P Selecting calculator modes~„p 23.0 Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Selecting Display modes Explanation of CAS settings Selecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW References Calculator objects Chapter Introducing the calculatorEditing expressions in the stack Creating arithmetic expressions Result³5*„Ü1+1/7will be shown„ÜR3as follows -2Q3`.5 Resulting…in³5*„Ü1+1/7the output„ÜR3-2Q3`.5 + y Creating algebraic expressions Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n Home directory Organizing data in the calculatorSubdirectories For this example, the Home Variables Locks the alphabetic keyboard in lower case. When lockedTyping variable names Creating variables Name Contents Type 3V5K~a12` ³~„r/„Ü ‚å‚é~„r³„ì Checking variables contents Using the right-shift key followed by soft menu key labels Using function Purge in the stack in RPN mode Using function Purge in the stack in Algebraic modeDeleting variables @PURGE@J@@p1@@` Choose boxes vs. Soft Menu Undo and CMD functionsWe use Show Prog menu list and select Memory ‚¯ Page Not shown in this screen. To Find it we use Display now shows To activate the Order command we press the soft menu key Chapter Calculations with real numbers Operation key, namely Examples in ALG modeExamples of real number calculations Directly on the stack For both, ALG and RPN modes, using the Equation Writer Key. When Combination When calculating in the stack in ALG modeRPN mode, enter the number first, then the function, e.g „¸Page \„¸45`‚¹ RPN mode Hyperbolic functions and their inverses Real number functions in the MTH menu Pressing shows the remaining options Units menu With unitsKey or Page For Set of units Available unitsLabels will be listed Key or Keystroke sequence to navigate Through the menus With the keyboard, e.g.,will produce the entry Attaching units to numbers Operations with units Using Ubase to convert to the default unit 1 m results 12m 3250mi Different terms in parentheses, e.g Physical constants in the calculator @@OK@@-˜Unit conversions These operations produce the following output When selected, constants are shown without units When selected, constants are shown with units attachedCopies value with or without units to the stack Exit constants library Like this Display shows what is called a tagged value Here Defining and using functionsWhich produces ‘LNx+1 + EXPx’ ‚@@@H@@ You could try Entered by using To work with complex numbers select the CAS complex mode Setting the calculator to Complex modeChapter Calculations with complex numbers Definitions Polar representation of a complex number Entering complex numbersTo enter the unit imaginary number type the I key Simple operations with complex numbers Cmplx menu through the MTH menu Cmplx menus Cmplx menu in the keyboard Function Droite equation of a straight line Functions applied to complex numbers Reference Function Droite is found in the command catalog Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Variable menu Press To recover Functions in the ALG menu @HELP@` Catalog To complete the operation To execute the command Expansion and factoring using trigonometric functions Expansion and factoring using log-exp functionsTrig menu, triggered by using Operations with transcendental functions Shows the following menu Functions in the Arithmetic menuNumbers or to polynomials. The remaining options 1. Integer Horner function PolynomialsX6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 Pcoef function VariableProot function Quotient and Remainder functions Peval function FractionsSIMP2 function Partfrac function Propfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Zeros Function Solvevx Numerical solver menu Enter vector of coefficients Polynomial EquationsSolve equation Page Page Solving equations with one unknown through NUM.SLV Financial calculations Solution shown is X 4.5006E-2 Solution to simultaneous equations with MslvPage Reference Creating and storing lists Chapter Operations with listsChanging sign Addition, subtraction, multiplication, division Functions‚Napplied to lists When applied to lists, acts a concatenation operatorExample Lists of algebraic objects Lists of complex numbersMTH/LIST menu Inverse 1/x Calculate summation of elements in the list Calculate increment among consecutive elements in listCalculate product of elements in the list Sorts elements in increasing order SEQ function SEQ function, available through the command catalog , takesMAP function Reference Entering vectors Chapter VectorsTyping vectors in the stack General row vector Vector Vector of algebraics Vectors can also be entered by using the matrix writer Mode Then, ‚íinStoring vectors into variables in the stack Stored into variables WID Key is used to edit the contents of a selected cell Cell of the spreadsheet Key will add a column full of zeros at the locationFunction Delete Will delete Selected Addition, subtraction Simple operations with vectorsUsed in the following exercises Absolute value function Multiplication by a scalar, and division by a scalar Magnitude MTH/VECTOR menuDot product Examples Cross product Entering matrices in the stack Chapter Matrices and linear algebra Typing in the matrix directly into the stack Display in RPN mode will look very similar to these Addition and subtraction Operations with matrices RPN mode, try the following eight examples Multiplication Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Characterizing a matrix The matrix Norm menu Solution of linear systemsFunction DET Function Trace Press Following input form will be provide right Using the numerical solver for linear systems2x1 + 3x2 -5x3= Can be written as the matrix equation A⋅x = b, if @SOLVE Solution by division of matrices Solution with the inverse matrix Graphs options in the calculator Chapter Graphics Plotting an expression of the form y = fx Them simultaneously if in RPN mode Use a range of -4 toAs an example, lets plot the function Also, check that for x = -1.48 , y = To recover the menu, and return to the PlotHere is picture Press Then Zoom factor = 0.5. Toggle You will be returned to normal calculator displayTo see the table, press Soft menu key Suggested early, namely x = Key simply changes the font in the table from small to big, Fast 3D plotsOption Decimal Produces x-increments Option Integer To return to normal calculator display press Values of 10 and 8 for the Step data Find Fast3DYou can change Orientation @EDITL Press To leave the Edit environment Reference$ Calc Calculus menu Chapter Calculus ApplicationsLimits and derivatives Function lim Including some limits Infinity symbol is associated with Key, .eMenu within the Calcl menu Functions INT, INTVX, RISCH, Sigma and Sigmavx Anti-derivatives and integralsIf and only if, fx = dF/dx, and C = constant Xdx = F b − F a ⋅ x − x o n Functions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Y dA = b Φ x , y dydx = Multiple integrals Del operator Chapter Vector Analysis ApplicationsGradient Curl DivergenceAlternatively, use function Deriv as follows Chapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Ldec Which can be simplified to Function Desolve= K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 DESOLVE` Variable Odetype Laplace transform and inverses in the calculator Laplace Transforms Fourier series for a quadratic function Function FOURIER`Where Exercises. Function Collect is available in the ALG menu Thus = 1/3, c MTH/PROBABILITY.. sub-menu part Chapter Probability DistributionsFactorials, combinations, and permutations Random numbers „´The Normal distribution MTH/PROB menu partStudent-t distribution F distribution Chi-square distribution Entering data‚Ù5 Chapter Statistical Applications Now Sample vs. population Obtaining frequency distributions Ƒ3.Fitdata Fitting data to a function y = fxCan be used Lines in RPN mode To access the summary stats… option, use When that field is selected StatisticsUsing Key select all the options for outputs, i.e Obtaining additional summary statistics Press to obtain the following results Confidence intervalsOffers the following options Interpreted as follows Interval information @GRAPH Return to the previous results screen, and/or press Corresponding interval limits 21.88424 and 24.51576. Press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is Base menu Chapter Numbers in Different BasesWriting non-decimal numbers With system flag 117 set to Soft menus, the Base menu shows @HEX Chapter Using SD cardsStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD card Limited Warranty Service Rotc = Rest of the country Canada 905 206-4663 or 800- HP USA Regulatory information