Matrix Operations

The calculator supports matrices and the most common matrix operations. Operations unique to Matrices, such as calculating the transpose and determinant, are contained under the "Matrix..." sub-menu button in the Special Menu. Other operations, such as addition, subtraction, multiplication and inversion, may be performed by using the normal calculator operations on matrix entries.

The Matrix... Sub-Menu

The matrix sub-menu is accessed by selecting the "Matrix..." button in the "Special" menu.

{{}{}}→M [ListToMatrix]

This is the command used to create a new matrix. It converts a list of lists into a matrix, where each sublist represents a row in the matrix. For example:

{{1, 3, 3}, {1, 4, 3}, {1, 3, 4}} or {(1, 3, 3), (1, 4, 3), (1, 3, 4)} - both are equivalent-

Becomes a matrix looking like this:

Notes: Column matrices may be entered as { 1 2 3 }. A row matrix may be entered as {{ 1 2 3 }}. It is possible to cut and paste comma separated values into lists, but it is necessary to include spaces after the commas or the calculator confuses the commas with grouping marks or decimals, depending on settings. Also spaces or semi-colons may be used as list separators.

M→{{}{}} [MatrixToList]

This command converts a matrix into a list of lists, where each sublist corresponds to a row in the matrix.

|M| [Determinant]

Finds the determinant of a matrix (matrix must be square).

M^-1 [MatrixInverse]

Inverts a matrix (matrix must be square). Can also be executed by using the "1/x" command in the main menu. Matrix inversion is done using Gauss-Jordan Elimination with Partial Pivoting.

M^-T [Transpose]

Transposes a matrix.

Solve

Solves a matrix using Gauss-Jordan Elimination with Partial Pivoting. The resulting matrix will be the identity matrix with an additional column containing the solution value for each variable (if the equation is solvable).

Normal Operations Performable on Matrices

Matrix Multiplication and Inversion

These two operations are treated in a unique fashion when they are used upon Matrices.

• A multiplication of two matrices is treated as a cross product.
• The reciprocal operator, "1/x", when performed on a matrix results in matrix inversion (note that there is also a matrix inversion option under the "Matrix..." menu).

Other Matrix Operations

Pretty much all of the calculator operations may be performed upon matrix entries. Note that except for multiplication and inversion, the result will generally be what would be expected from performing the regular scalar operation on matching entries within the matrix - as opposed to some special result for matrices. To address the individual cases:

Single Matrix

Operations that normally take a single entry (sqrt, sin, etc.) will be performed upon each individual entry inside the target matrix.

Two Matrices

Operations that normally take two entries (+, -, x^y, etc.) will be performed upon each corresponding pair of entries within the two matrices. The matrices must be equal in size or the result will be an error message.

Scalar and a Matrix

Operations that normally take two entries (+, -, x^y, etc.) will be performed the single scalar value and each value within the target matrix. The scalar value and the matrix value may be on the stack in either order, depending on which is to be treated as the first operand.