Review Exercises for

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Chapter 3 Summary True/False Quiz Index of Review Exercises Everything for Calculus Everything for Finite Math Everything for Finite Math & Calculus Utility: Matrix Algebra Tool Download: Matrix Software for Mac 
Let A  = 

,  B  = 

,  C  = 

,  and D  = 

. 
For each of the following, determine whether the expression is defined, and if it is, evaluate it.
1.  A + C  Answer (if defined): 


2.  A  C^{T}  Answer (if defined): 


3.  C^{T} + 3D  Answer (if defined): 


4.  BA  Answer (if defined): 


5.  BA^{T}  Answer (if defined): 


6.  BC  Answer (if defined): 


7.  CB  Answer (if defined): 


8.  B^{4}  Answer (if defined): 


9.  AA^{T}  Answer (if defined): 


10.  D^{T}D  Answer (if defined): 

For each of the given matrices, find the inverse or determine that the matrix is singular.
11. 

Inverse (if defined): 


12. 

Inverse (if defined): 


13. 

Inverse (if defined): 


14. 

Inverse (if defined): 


15. 

Inverse (if defined): 


16. 

Inverse (if defined): 

Write each of the following systems of linear equations as a matrix equation, and solve by inverting the coefficient matrix.