Page 125 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

T1. Matrix Operations Read your documentation on how to perform the basic operations on matrices—addition, subtraction,
multiplication by scalars, and multiplication of matrices. Then perform the computations in Examples Example 3, Example 4,
and Example 5. See what happens when you try to perform an operation on matrices with inconsistent sizes.

Evaluate the expression for the matrix
T2.

T3. Extracting Rows and Columns Read your documentation on how to extract rows and columns from a matrix, and then use
your utility to extract various rows and columns from a matrix of your choice.

T4. Transpose and Trace Read your documentation on how to find the transpose and trace of a matrix, and then use your utility
to find the transpose of the matrix A in Formula (12) and the trace of the matrix B in Example 12.

T5. Constructing an Augmented Matrix Read your documentation on how to create an augmented matrix from matrices

A and b that have previously been entered. Then use your utility to form the augmented matrix for the system in

Example 4 of Section 1.1 from the matrices A and b.

Section 1.4

T1. Zero and Identity Matrices Typing in entries of a matrix can be tedious, so many technology utilities provide shortcuts for
entering zero and identity matrices. Read your documentation on how to do this, and then enter some zero and identity
matrices of various sizes.

T2. Inverse Read your documentation on how to find the inverse of a matrix, and then use your utility to perform the
computations in Example 7.

T3. Formula for the Inverse If you are working with a CAS, use it to confirm Theorem 1.4.5.

T4. Powers of a Matrix Read your documentation on how to find powers of a matrix, and then use your utility to find various
positive and negative powers of the matrix A in Example 8.

Let
T5.

Describe what happens to the matrix when k is allowed to increase indefinitely (that is, as ).