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HP 50g manual Operations with matrices

Models: 50g

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Operations with matrices

Matrices, like other mathematical objects, can be added and subtracted. They can be multiplied by a scalar, or among themselves, and raised to a real power. 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 (The random matrices in your calculator may be different):

In RPN mode, the steps to follow are:

{2,2}`RANM 'A22'`K{2,2}`RANM 'B22'`K {2,3}`RANM 'A23'`K{2,3}`RANM 'B23'`K {3,2}`RANM 'A32'`K{3,2}`RANM 'B32'`K {3,3}`RANM 'A33'`K{3,3}`RANM 'B33'`K

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HP 50g manual Operations with matrices

Contents

HP 50g graphing calculator User’s manual Printing History Preface 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 Applications Multi-variateCalculus Applications Vector Analysis ApplicationsDifferential Equations Probability Distributions Using SD cards Statistical ApplicationsNumbers in Different Bases Equation Library Batteries Chapter Getting startedBasic Operations Page Tool menu Contents of the calculator’s displayMenus Setting time and date Introducing the calculator’s keyboard ALPHA-Left-Shift function, to enter the lower-case letter p Selecting calculator modes Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5Page Lets try now the expression proposed earlier Fixed format with decimals Number Format and decimal dot or commaStandard format Scientific format Engineering format Decimal comma vs. decimal point 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 expressionsPage Page Creating algebraic expressions 2L 1 + + 2 L + y Using the Equation Writer EQW to create expressions + 2 ⋅ 5 + ⎛ x + 2 ∝ ⋅ ∆y ⎞ Organizing data in the calculator Home directory Typing variable names VariablesSubdirectories Algebraic mode Creating variables RPN mode Page Checking variables contents Deleting variables Listing the contents of all variables in the screenUsing function Purge in the stack in Algebraic mode Using function Purge in the stack in RPN mode Undo and CMD functions Choose boxes vs. Soft Menu @@OK@@ References Chapter Calculations with real numbers Examples of real number calculationsPage Using powers of 10 in entering data Page Hyperbolic functions and their inverses Using calculator menusReal number functions in the MTH menu Page Operations with units Units menuPage Available units Attaching units to numbers Unit prefixes Operations with units Unit conversions Physical constants in the calculator QuitPage Defining and using functions Reference Definitions Setting the calculator to Complex modeChapter Calculations with complex numbers Entering complex numbers Polar representation of a complex number Cmplx menu through the MTH menu Simple operations with complex numbersCmplx menus Forms the complex number x,y out of real numbers x Functions applied to complex numbers Cmplx menu in keyboard Function Droite equation of a straight line Page Chapter Algebraic and arithmetic operations Entering algebraic objects Simple operations with algebraic objects Functions in the ALG menu Collect Expansion and factoring using log-exp functions Operations with transcendental functions Expansion and factoring using trigonometric functions Functions in the Arithmetic menu FACTORSSIMP2 Polynomials Horner functionVariable Pcoef function Fractions Proot functionQuot and Remainder functions Peval function SIMP2 function Propfrac functionPartfrac function Fcoef function − 5X 2 + 3X − Step-by-step operations with polynomials and fractionsFroots function Reference Function Isol Chapter Solution to equationsSymbolic solution of algebraic equations Function Solve Page Function Solvevx Function Zeros Numerical solver menu Finding the solutions to a polynomial equation Polynomial Equations Enter vector of roots Financial calculations Generating an algebraic expression for the polynomial Solving equations with one unknown through Function Steq Solution to simultaneous equations with Mslv Reference Page Chapter Operations with lists Creating and storing listsOperations with lists of numbers Changing sign Addition, subtraction, multiplication, division Page Lists of complex numbers Functions applied to lists Lists of algebraic objects MTH/LIST menuPage SEQ function MAP functionPage Typing vectors in the stack Chapter VectorsEntering vectors Storing vectors into variables in the stack Using the Matrix Writer Mtrw to enter vectors Moving to the right vs. moving down in the Matrix Writer Press @GOTO@ 3@@OK@@ 3@@OK@@ @@OK@@ to move to position 3,3 Simple operations with vectors Addition, subtraction Absolute value function MTH/VECTOR menuMultiplication by a scalar, and division by a scalar Cross product MagnitudeDot product Reference Entering matrices in the stack Using the Matrix WriterChapter Matrices and linear algebra Typing in the matrix directly into the stack Operations with matrices Multiplication by a scalar Addition and subtractionMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Matrix-vector multiplicationMatrix multiplication Raising a matrix to a real power Term-by-term multiplication Identity matrix Inverse matrix Characterizing a matrix The matrix Norm menu Function DETFunction Trace TrA = ∑aii Solution of linear systems Using the numerical solver for linear systems = ⎢1 ⎢x2 Solution with the inverse matrix Solution by division of matrices References Chapter Graphics Graphs options in the calculator Plotting an expression of the form y = fx = 1 exp− xPage Generating a table of values for a function Fast 3D plots Keep the default plot window ranges to read Reference Page Chapter Calculus Applications Calc Calculus menuLimits and derivatives Function lim Lim f Anti-derivatives and integrals Functions Deriv and DervxFunctions INT, INTVX, RISCH, Sigma and Sigmavx Xdx = F x + C Definite integrals = ∑ Infinite seriesFunctions TAYLR, TAYLR0, and Series Reference Chapter Multi-variate Calculus Applications Partial derivatives Multiple integrals Gradient Chapter Vector Analysis ApplicationsDel operator Divergence Curl Solution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Function LdecPage Function Desolve Variable Odetype Laplace Transforms Laplace transform and inverses in the calculator Fourier series Function FourierLf t= F s = 0∞ f t ⋅ e− st dt 2inπt Fourier series for a quadratic function Reference Page Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations − r + Random numbers Student-t distribution MTH/PROB menu partNormal distribution Chi-square distribution F distribution Chapter Statistical Applications Entering data Calculating single-variable statistics Sample vs. population Obtaining frequency distributions Page Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Page Chapter Numbers in Different Bases Base menu Writing non-decimal numbers Formatting an SD card Chapter Using SD cardsInserting and removing an SD card Accessing objects on an SD card Storing objects on the SD card Recalling an object from the SD card Purging an object from the SD card Purging all objects on the SD card by reformatting Specifying a directory on an SD card Chapter Equation Library `#EQLIB #EQNLI Step 30 ##¢0#- L *!!!!!!V0!!!!!+ Reference Limited Warranty W-2 Service Europe Asia Pacific Country Telephone numbers America Country Telephone numbers Regulatory information Federal Communications Commission Notice Canadian Notice Korean Notice