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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 =
A
−1
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