Operations with matrices, Addition and subtraction | HP 49g manual

Operations with matrices

Matrices, like other mathematical objects, can be added and subtracted. They can be multiplied by a scalar, or among themselves. An important operation for linear algebra applications is the inverse of a matrix. Details of these operations are presented next.

To illustrate the operations we will create a number of matrices that we will store in the following variables. Here are the matrices A22, B22, A23, B23,

A33 and B33:

In RPN mode, the steps to follow are:

2,2}	2		2,	2
{3,3}		2'	2}	2'

`RANM'A33'`K{3,3}`RANM'B33'`K

Addition and subtraction

Four examples are shown below using the matrices stored above (ALG mode).

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HP 49g manual Operations with matrices, Addition and subtraction

Contents

User’s manual Graphing calculatorPage Preface Page Table of Contents Calculations with real numbers Calculations with complex numbers Algebraic and arithmetic operations Solution to equations Operations with lists Vectors Matrices and linear algebra Graphics Calculus ApplicationsMulti-variate Calculus Applications Vector Analysis Applications Differential Equations Probability DistributionsStatistical Applications Limited Warranty W-1 Service, W-2 Regulatory information, W-4Numbers in Different Bases Chapter Getting started Basic OperationsBatteries Contents of the calculator’s display Menus Tool menuAssociated with the six soft menu keys, F1 through F6 Setting time and date Introducing the calculator’s keyboardPage Selecting calculator modes Alpha function, to enter the upper-case letter P~„p Operating Mode 23.0 √ 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 Explanation of CAS settings Selecting Display modes Selecting the display font Selecting properties of the line editor Selecting properties of the Stack References Selecting properties of the equation writer EQW Chapter Introducing the calculator Calculator objectsEditing 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 Creating algebraic expressions + y Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n Organizing data in the calculator Home directorySubdirectories For this example, the Home Locks the alphabetic keyboard in lower case. When locked VariablesTyping variable names Name Contents Type Creating variables 3V5K~a12` ³~„r/„Ü Checking variables contents ‚å‚é~„r³„ì Using the right-shift key followed by soft menu key labels Using function Purge in the stack in Algebraic mode Using function Purge in the stack in RPN modeDeleting variables @PURGE@J@@p1@@` Undo and CMD functions Choose boxes vs. Soft MenuWe use Show Prog menu list and select Memory ‚¯ Page Display now shows Not shown in this screen. To Find it we use To activate the Order command we press the soft menu key Operation key, namely Examples in ALG mode Chapter Calculations with real numbersExamples of real number calculations For both, ALG and RPN modes, using the Equation Writer Directly on the stack Combination When calculating in the stack in ALG mode Key. WhenRPN mode, enter the number first, then the function, e.g „¸Page RPN mode \„¸45`‚¹ Real number functions in the MTH menu Hyperbolic functions and their inverses Pressing shows the remaining options With units Units menuKey or Page Available units For Set of unitsLabels will be listed Key or Keystroke sequence to navigate Through the menus Attaching units to numbers With the keyboard, e.g.,will produce the entry Using Ubase to convert to the default unit 1 m results Operations with units Different terms in parentheses, e.g 12m 3250mi @@OK@@-˜ Physical constants in the calculatorUnit conversions These operations produce the following output When selected, constants are shown with units attached When selected, constants are shown without unitsCopies value with or without units to the stack Exit constants library Defining and using functions Like this Display shows what is called a tagged value HereWhich produces ‚@@@H@@ ‘LNx+1 + EXPx’ Entered by using You could try Setting the calculator to Complex mode To work with complex numbers select the CAS complex modeChapter Calculations with complex numbers Definitions Entering complex numbers Polar representation of a complex numberTo enter the unit imaginary number type the I key Simple operations with complex numbers Cmplx menus Cmplx menu through the MTH menu Cmplx menu in the keyboard Functions applied to complex numbers Function Droite equation of a straight line Function Droite is found in the command catalog Reference Chapter Algebraic and arithmetic operations Entering algebraic objects Simple operations with algebraic objects Press To recover Variable menu @HELP@` Functions in the ALG menu To execute the command Catalog To complete the operation Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functionsTrig menu, triggered by using Operations with transcendental functions Functions in the Arithmetic menu Shows the following menuNumbers or to polynomials. The remaining options 1. Integer Polynomials Horner functionX6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 Variable Pcoef functionProot function Quotient and Remainder functions Fractions Peval functionSIMP2 function Propfrac function Partfrac functionFcoef function Step-by-step operations with polynomials and fractions Froots function Reference Chapter Solution to equations Symbolic solution of algebraic equationsFunction Isol Function Solve Page Function Solvevx Function Zeros Numerical solver menu Polynomial Equations Enter vector of coefficientsSolve equation Page Page Financial calculations Solving equations with one unknown through NUM.SLV Solution to simultaneous equations with Mslv Solution shown is X 4.5006E-2Page Reference Chapter Operations with lists Creating and storing listsChanging sign Addition, subtraction, multiplication, division When applied to lists, acts a concatenation operator Functions‚Napplied to listsExample Lists of complex numbers Lists of algebraic objectsMTH/LIST menu Inverse 1/x Calculate increment among consecutive elements in list Calculate summation of elements in the listCalculate product of elements in the list Sorts elements in increasing order SEQ function, available through the command catalog , takes SEQ functionMAP function Reference Chapter Vectors Entering vectorsTyping vectors in the stack General row vector Vector Vector of algebraics Mode Then, ‚íin Vectors can also be entered by using the matrix writerStoring vectors into variables in the stack Stored into variables Key is used to edit the contents of a selected cell WID Key will add a column full of zeros at the location Cell of the spreadsheetFunction Delete Will delete Selected Simple operations with vectors Addition, subtractionUsed in the following exercises Multiplication by a scalar, and division by a scalar Absolute value function MTH/VECTOR menu MagnitudeDot product Examples Cross product Chapter Matrices and linear algebra Entering matrices in the stack Display in RPN mode will look very similar to these Typing in the matrix directly into the stack Operations with matrices Addition and subtraction Multiplication RPN mode, try the following eight examples Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Solution of linear systems Characterizing a matrix The matrix Norm menuFunction DET Function Trace Using the numerical solver for linear systems Press Following input form will be provide right2x1 + 3x2 -5x3= Can be written as the matrix equation A⋅x = b, if @SOLVE Solution with the inverse matrix Solution by division of matrices Chapter Graphics Graphs options in the calculator Them simultaneously if in RPN mode Use a range of -4 to Plotting an expression of the form y = fxAs an example, lets plot the function To recover the menu, and return to the Plot Also, check that for x = -1.48 , y =Here is picture Press Then You will be returned to normal calculator display Zoom factor = 0.5. ToggleTo see the table, press Soft menu key Suggested early, namely x = Fast 3D plots Key simply changes the font in the table from small to big,Option Decimal Produces x-increments Option Integer To return to normal calculator display press Find Fast3D Values of 10 and 8 for the Step dataYou can change Orientation @EDITL Reference$ Press To leave the Edit environment Chapter Calculus Applications Calc Calculus menuLimits and derivatives Function lim Infinity symbol is associated with Key, .e Including some limitsMenu within the Calcl menu Anti-derivatives and integrals Functions INT, INTVX, RISCH, Sigma and SigmavxIf and only if, fx = dF/dx, and C = constant Xdx = F b − F a Functions TAYLR, TAYLR0, and Series ⋅ x − x o n Reference Chapter Multi-variate Calculus Applications Partial derivatives Multiple integrals Y dA = b Φ x , y dydx = Chapter Vector Analysis Applications Del operatorGradient Divergence CurlAlternatively, use function Deriv as follows Solution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Ldec Function Ldec Function Desolve Which can be simplified to= K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 Variable Odetype DESOLVE` Laplace Transforms Laplace transform and inverses in the calculator Function FOURIER` Fourier series for a quadratic functionWhere Exercises. Function Collect is available in the ALG menu Thus = 1/3, c Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations Random numbers MTH/PROB menu part „´The Normal distributionStudent-t distribution Chi-square distribution F distribution Chapter Statistical Applications Entering data‚Ù5 Sample vs. population Now Obtaining frequency distributions Fitting data to a function y = fx Ƒ3.FitdataCan be used Lines in RPN mode When that field is selected Statistics To access the summary stats… option, useUsing Key select all the options for outputs, i.e Obtaining additional summary statistics Confidence intervals Press to obtain the following resultsOffers the following options Interpreted as follows @GRAPH Interval information Corresponding interval limits 21.88424 and 24.51576. Press Return to the previous results screen, and/or press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is Chapter Numbers in Different Bases Base menuWriting non-decimal numbers With system flag 117 set to Soft menus, the Base menu shows @HEX Using SD cards ChapterStoring objects in the SD card Recalling an object from the SD card Purging an object from the SD card Limited Warranty Service Canada 905 206-4663 or 800- HP Rotc = Rest of the country Regulatory information USA