HP -42S Calculator Manual: Your Complete Resource for the 42S

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Exercise: Calculate the determinant of this matrix:

First line: 1 2 3

Second line: -2 3 5

Third line: 0 4 -1

Solution: First we create a 3x3 matrix

3 ENTER ▀ MATRIX NEW

We have x: [ 3x3 Matrix] in the display

Now we press EDIT and we have 1:1=0.0000 Let's enter all elements. (First line)

1 → 2 → 3

Let's go, for example to (2,1), to enter the second line. ↓ ← ←

2 +/- → 3 →5 ↓ ← ←

0 → 4 →1 +/-

Then we press exit to stop editing. Now to calculate the determinant is just press DET which gives -51. (if you are going to use the same matrix again you'd better save it before any calculation)

One cannot create any size of matrix because we are limited by the available memory of the calculator. In my palm tungsten E using Free42 I can create a matrix of 90x90 and in my PC the Free42 program can give me a 5000x5000 or bigger while in the real HP-42S is 29x29.

The EDIT function is not useful only to enter a matrix but also to see all the elements of matrix resultant from a calculation. Talking about matrix calculation, the HP-42S does +, -, x and ÷ of matrices in normal way. Of course, as you know, the operations are not always possible. For example: To sum or subtract matrices they must have the same size, etc.

How can one use matrices to solve linear systems? The HP-42S owner's manual explains it by using the SIMQ function.

But it would be more profitable to remember a little of linear algebra. If you have nxn linear system you can always write it as the matrix equation

A X = B

where A is nxn matrix called the coefficient matrix, B is nx1 column matrix called independent terms matrix and X is also a nx1 column matrix which contains the unknown variables.

By multiplying this equation by the inverse matrix of A we have

X = A1 B.

So if you are able to perform the inverse of matrix and able to multiply matrices you can solve a linear system without needing to learn another calculator's function.

What about complex matrices? You cannot enter complex numbers in a normal matrix. You have to create a complex matrix first. The procedure to do this is like to create a complex number. First

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Contents An alternative HP-42S/Free42 Manual Version 2005 Index Introduction RPN Basic OperationsTurn ON/OFF Setting the display contrastTraining RPN using HP-42S FIX, SCI, ENG, ALL, RDX., RDX MenusPage Stack Modes MenuGetting used to some keys of the keyboard Page Abcde Fghi Jklm Nopq Rstuv Wxyz Memory More on the Clear menu Catalog menuAssign ABS to Custom menuAssign FCN ABS Probability Where N!=N.N-1.N-2...2.1Page Complex numbers in polar coordinates Complex NumbersComplex numbers in rectangular coordinates Basic programming Programming19STOP More than one program in the memory X?0 and X?Y sub-menus EnterSqrt Real program examplesLBL Prime Select Solve Program Using the SolverPage Ba f  xdx Numeric IntegrationSub-menu Cfit StatisticsEnter 6 Σ+ Second line ALLΣ, LINΣ, Σreg and ΣRG? Functions Matrices = B Enter Matrix NEWMatrix 1 Enter 3 NEW Enter NEW Enter ComplexEnter 3 NEW Edit 1 Enter →→5 +/- Enter Exit STO B RCL a RCL B Matrix CrossOther Bases Flags License