Linear Algebra (Math 220)
Assignment due Thursday, March 6

1.  Preparation

Expect a quiz.

Suggested Reading:

• Lay §§ 4.4 – 4.6

• Hefferon §§ 3.III – 3.IV

2.  Exercises

1. Find the inverse, if it exists, of the $4\times 4$ matrix $$\left(\begin{array}{cccc}\hfill 1& \hfill 2& \hfill 1& \hfill 2\\ \hfill -2& \hfill -1& \hfill 3& \hfill 2\\ \hfill -2& \hfill 2& \hfill 6& \hfill -1\\ \hfill 1& \hfill 0& \hfill -2& \hfill 0\end{array}\right)$$

2. For each of the following $4\times 4$ matrices find (a) the rank of the matrix and (b) non-redundant sets of linear equations in $4$ variables that characterize the linear relations among the rows of the matrix.

   1. $$\left(\begin{array}{cccc}\hfill 1& \hfill 2& \hfill -4& \hfill 7\\ \hfill -2& \hfill -1& \hfill -1& \hfill -8\\ \hfill 5& \hfill 7& \hfill -11& \hfill 29\\ \hfill -1& \hfill -4& \hfill -14& \hfill 5\end{array}\right)$$

   2. $$\left(\begin{array}{cccc}\hfill 1& \hfill 2& \hfill -4& \hfill 7\\ \hfill -2& \hfill -1& \hfill -1& \hfill -8\\ \hfill 5& \hfill 7& \hfill -11& \hfill 29\\ \hfill -3& \hfill -6& \hfill 12& \hfill -21\end{array}\right)$$

   3. $$\left(\begin{array}{cccc}\hfill 1& \hfill 2& \hfill -4& \hfill 7\\ \hfill -2& \hfill -1& \hfill -1& \hfill -8\\ \hfill 5& \hfill 7& \hfill -11& \hfill 29\\ \hfill -1& \hfill -4& \hfill -14& \hfill 0\end{array}\right)$$