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# Gaussian Elimination of Matrices on HP Prime Graphing Calculator

A. Looking for key strokes to put matrices operators together to conduct a Gaussian Elimination of a Matrix, typically a 3 x 3. Tried the ref(M6), but returned incomprehensible answers. Please advise.  Chapter 26 in the user guide.

B.  Is it possible to download the Prime Graphing Calculator off the website -- I have the CD.  Also, should I be updating OS or firmware if I recently purchased it.

Thanks.

Chappie_1

# Re: Gaussian Elimination of Matrices on HP Prime Graphing Calculator

Thanks for everyone's time and great answers. First you have to know how to do one, sort of.

A. Goal is to have positive 1's along the diagonal and B. Kill everything with zeros below the diagonal, except last value.  This can be done with SCALE and SCALEADD commands.

Not really writing programs. Enter matrix into the a designated matrix -- just pick one. Get into CAS and pull up menu of matrix commands or type in SCALE and SCALEADD.

SCALE (Matrix name, factor to multiply by, row number) first to achieve A.

SCALEADD (Matrix name, factor to multiply, to which row, and added to which row) to achieve B.

Delimiter commas are needed.

For a augmented matrix with integer solutions, agree the RREF gives the anwer immediately.

Then you can back subsitute to solve for other coefficients.

Other tips for matrix solutions, the M#(Row #, Col #) gives the value in that location.  The Cholesky command, gives the U-transpose and transpose of that gives U. Eigenvalue and Eigenvector commands also very cool.

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## Re: Gaussian Elimination of Matrices on HP Prime Graphing Calculator

A. RREF (instead of ref) might be what you need.  However, RREF(3×3) will always return an identity matrix, so you'll want to use an augmented matrix, e.g. 3×4.

B. Install the Connectivity Kit from your CD and then run it to update itself.  Then connect your calculator (via USB cable) and the the Connectivity Kit update it also.  It'll know whether or not these respective updates are available, and they are, yes, you should update, to access recent improvements and eliminate bugs.  The "Virtual Calculator" program is able to update itself.  Having recently bought your Prime doesn't mean that its firmware is up to date, since it may have been "in the pipeline" for a while.

-Joe-
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## Re: Gaussian Elimination of Matrices on HP Prime Graphing Calculator

Chappie_1 wrote:

A. Looking for key strokes to put matrices operators together to conduct a Gaussian Elimination of a Matrix, typically a 3 x 3. Tried the ref(M6), but returned incomprehensible answers. Please advise.  Chapter 26 in the user guide.

The Prime offers a lot of commands for matrix manipulation and elimination.

When you are writing a program you are in the program editor.

In its menu choose: cmds - Matrix - SCALE

This command multiplies the specified row of your matrix by a certain value.

Choose cmds - Matrix - SCALEADD

This command multiplies the specified row by a certain value and adds it to another row.

So thus we can create a zero in our matrix.

Now go to Toolbox – Math – Matrix – Basic – pivot.

This command uses Gaussian elimination to return a matrix with all zeros in a certain column, except one.

I did not know ref, but it uses Gaussian reduction to create an echelon matrix having rows which all start with 1.

Note that this matrix is not unique, so you might expect something else.

The strongest command is RREF, which uses gaussian elimination to find a unique matrix, with all rows starting with 1, which is the only non – zero element in its column.

For a 3 by 3 matrix this is often the identity matrix, but not always.

When it is the identity matrix this means that the corresponding system of 3 homogeneous equations has only the zero solution.

When it is not the identity matrix it means there is another solution, which you can easily get now.

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Member Since: ‎02-22-2017
Message 4 of 4 (258 Views)

## Re: Gaussian Elimination of Matrices on HP Prime Graphing Calculator

[ Edited ]

Thanks for everyone's time and great answers. First you have to know how to do one, sort of.

A. Goal is to have positive 1's along the diagonal and B. Kill everything with zeros below the diagonal, except last value.  This can be done with SCALE and SCALEADD commands.

Not really writing programs. Enter matrix into the a designated matrix -- just pick one. Get into CAS and pull up menu of matrix commands or type in SCALE and SCALEADD.

SCALE (Matrix name, factor to multiply by, row number) first to achieve A.

SCALEADD (Matrix name, factor to multiply, to which row, and added to which row) to achieve B.

Delimiter commas are needed.

For a augmented matrix with integer solutions, agree the RREF gives the anwer immediately.

Then you can back subsitute to solve for other coefficients.

Other tips for matrix solutions, the M#(Row #, Col #) gives the value in that location.  The Cholesky command, gives the U-transpose and transpose of that gives U. Eigenvalue and Eigenvector commands also very cool.

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