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By experimenting with different values of n, find an expression for the inverse of an matrix of the form
T6.
Section 1.5
Use your technology utility to verify Theorem 1.5.1 in several specific cases.
T1.
T2. Singular Matrices Find the inverse of the matrix in Example 4, and then see what your utility does when you try to invert
the matrix in Example 5.
Section 1.6 by Inversion Use the method of Example 4 to solve the system in Example 3 of Section 1.1.
T1. Solving
Compare the solution of by Gaussian elimination and by inversion for several large matrices. Can you see the
T2. superiority of the former approach?
Solve the linear system , given that
T3.
Section 1.7
T1. Diagonal, Symmetric, and Triangular Matrices Many technology utilities provide short-cuts for entering diagonal,
symmetric, and triangular matrices. Read your documentation on how to do this, and then experiment with entering various
matrices of these types.
T2. Properties of Triangular Matrices Confirm the results in Theorem 1.7.1 using some triangular matrices of your choice.
Confirm the results in Theorem 1.7.4. What happens if A is not square?
T3.
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