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(a) Assume  →   → →  (b) →     →  . For
the value of det is zero which means
You can check the truth by plugging in the values and using Matlab/Octave. . Problem 3.
a. Row operations don’t change the determinant of a matrix. The resulting matrix is: 
 
 b. The resulting matrix is:

 c. The resulting matrix is lower triangular hence: 
 Problem 4.
(a) The corresponding matrix equation is:
[
This system has a unique solution iff

[ ] . Hence:  which always holds. Using Cramer’s Rule: ....
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 Fall '13
 KFOURY
 Algorithms

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