Matrices and Matrix Operations
                                 with
                            TI-Nspire™ CAS
                              Forest W. Arnold
                                June 2020
                              A
                       Typeset in LT X.
                                E
                       Copyright © 2020 Forest W. Arnold
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                             Attribution
              MostoftheexamplesinthisarticlearefromAFirstCourseinLinearAlgebraanOpen
              Text by Lyrix Learning, base textbook version 2017 - revision A, by K. Kuttler.
              The text is licensed under the Creative Commons License (CC BY) and is available
              for download at the link
              https://lyryx.com/first-course-linear-algebra/.
                              1    Introduction
                              Thearticle Systems of Equations with TI-Nspire™ CAS: Matrices and Gaussian Elim-
                              ination described how to represent and solve systems of linear equations with matrices
                              and elementary row operations. By defining arithmetic and algebraic operations with
                              matrices, applications of matrices can be expanded to include more than simply solving
                              linear systems.
                              Thisarticle describes and demonstrates how to use TI-Nspire’s builtin matrix functions
                              to
                                  • add and subtract matrices,
                                  • multiply matrices by scalars,
                                  • multiply matrices,
                                  • transpose matrices,
                                  • find matrix inverses, and
                                  • use matrix equations.
                              TheTI-Nspire examples in this article require the CAS version of TI-Nspire.
                              2    Matrices and Vectors
                              In TI-Nspire CAS, a matrix is a rectangular array of expressions (usually numbers)
                              with m rows and n columns. The dimension (size) of a matrix is denoted as m×n.
                              Whenstating the dimension of a matrix, m, the number of rows is always stated first.
                              Anexampleofa3×4matrixis
                                                                            
                                                           a    a     a    a
                                                            11    12   13   14
                                                                            
                                                           a    a     a    a                            (1)
                                                            21    22   23   24
                                                           a    a     a    a
                                                            31    32   33   34
                              Avector is either a matrix with one row and multiple columns (a row vector) or a
                              matrix with multiple rows and a single column (a column vector). An example of a
                              rowvector is
                                                                             
                                                           rv1  rv2   rv3  rv4                          (2)
                              and an example of a column vector is
                                                                     
                                                                   cv1
                                                                     
                                                                   cv2                                  (3)
                                                                   cv3
                                                                    1