Multiplication | HP 49g manual

In RPN mode, try the following eight examples:

A22 `B22`+ A22 `B22`-

A23 `B23`+ A23 `B23`-

A32 `B32`+ A32 `B32`-

A33 `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. A 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

Contents

Hp 49g+ 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 ApplicationsMulti-variate Calculus Applications Vector Analysis Applications Differential Equations Probability DistributionsStatistical Applications Using SD cards Limited Warranty W-1Numbers in Different Bases Chapter Getting started Basic OperationsBatteries Contents of the calculator’s display Menus Tool menu Setting time and date Introducing the calculator’s keyboardPage Selecting calculator modes 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 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 Page + 2 ⋅ 5 +  x + 2µ ⋅ ∆y  + e Organizing data in the calculator Home directorySubdirectories Variables Typing variable names Creating variables Page Page Checking variables contents Page Using function Purge in the stack in Algebraic mode Deleting variables Using function Purge in the stack in RPN mode Undo and CMD functionsChoose boxes vs. Soft Menu Show Prog menu list and select Memory Page References Chapter Calculations with real numbers Examples of real number calculationsPage Page Using powers of 10 in entering data Page Real number functions in the MTH menu Hyperbolic functions and their inversesPage Operations with units Units menuPage Available units Attaching units to numbers Operations with units Page Physical constants in the calculator Unit conversions Engl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Setting the calculator to Complex mode Chapter Calculations with complex numbersDefinitions Entering complex numbers Polar representation of a complex number Simple operations with complex numbers Cmplx menus Cmplx menu through the MTH menu Cmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight line Reference Chapter Algebraic and arithmetic operations Entering algebraic objects Simple operations with algebraic objects `‚¹ Functions in the ALG menu CollectPage Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functionsOperations with transcendental functions Functions in the Arithmetic menu Polynomials Horner function Variable Pcoef functionProot function Quot and Remainder functions Fractions Peval functionSIMP2 function Propfrac function Partfrac functionFcoef function Step-by-step operations with polynomials and fractions Froots function− 5X 2 + 3X − Reference Chapter Solution to equations Symbolic solution of algebraic equationsFunction Isol Function Solve Page Function Solvevx Function Zeros Numerical solver menu Polynomial Equations @SOLVE@ Solve for coefficients ˜@SYMB@ Financial calculations Solving equations with one unknown through NUM.SLV Solution to simultaneous equations with Mslv Page Reference Chapter Operations with lists Creating and storing listsOperations with lists of numbers Changing sign Addition, subtraction, multiplication, division Functions applied to lists Lists of complex numbers Lists of algebraic objectsMTH/LIST menu ∆LIST SEQ function MAP function Chapter Vectors Entering vectorsTyping vectors in the stack Using the Matrix Writer Mtrw to enter vectors Storing vectors into variables in the stackPage Page Simple operations with vectors Addition, subtraction Multiplication by a scalar, and division by a scalar Absolute value function MTH/VECTOR menu MagnitudeDot product Cross product Using the Matrix Writer Chapter Matrices and linear algebraEntering matrices in the stack Typing in the matrix directly into the stack Operations with matrices Addition and subtraction Multiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Solution of linear systems Characterizing a matrix The matrix Norm menuFunction DET Function Trace Using the numerical solver for linear systems =  a M x2 Solution with the inverse matrix Solution by division of matrices Chapter Graphics Graphs options in the calculator Plotting an expression of the form y = fx = 1 exp− x Generating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Chapter Calculus Applications Calc Calculus menuLimits and derivatives Function lim Functions Deriv and Dervx Anti-derivatives and integrals Xdx = F x + CFunctions INT, INTVX, RISCH, Sigma and Sigmavx Infinite series Definite integrals Functions TAYLR, TAYLR0, and Series Reference Chapter Multi-variate Calculus Applications Partial derivatives Multiple integrals Φ x, ydydx Chapter Vector Analysis Applications Del operatorGradient ∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂z Divergence Curl Solution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Function Ldec Function Desolve Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0 Variable Odetype Desolve Laplace Transforms Laplace transform and inverses in the calculator Fourier series = ∑ c nFunction Fourier Fourier series for a quadratic functionPage Reference Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations − 2... − + 1 = − r Random numbers MTH/PROB menu part Normal distributionStudent-t distribution Chi-square distribution F distribution Chapter Statistical Applications Entering dataCalculating single-variable statistics Page Obtaining frequency distributions Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Chapter Numbers in Different Bases Base menuWriting non-decimal numbers HEX DEC OCT BIN 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 HP Invent Regulatory information USA