added suggested gauss elimination

linear_algebra/gauss_suggested.md

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+# Linear Algebra Review 
+## (Gauss Elimination) Suggested problems
+### No due date
+
+1. Solve for x when Ax=b for the following problems:
+
+    a. $A=\left[ \begin{array}{cc}
+        1 & 3 \\
+        2 & 1 \end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        1 \\
+        1\end{array}\right]$
+
+    a. $A=\left[ \begin{array}{cc}
+        1 & 1 \\
+        2 & 3 \end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        3 \\
+        4\end{array}\right]$
+
+    a. $A=\left[ \begin{array}{cc}
+        1 & 1 \\
+        2 & -2 \end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        4 \\
+        2\end{array}\right]$
+
+    b. $A=\left[ \begin{array}{ccc}
+        1 & 3 & 1 \\
+        -4 & -9 & 2 \\
+        0 & 3 & 6\end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        0 \\
+        0 \\
+        0\end{array}\right]$
+
+    c. $A=\left[ \begin{array}{ccc}
+        1 & 3 & 1 \\
+        -4 & -9 & 2 \\
+        0 & 3 & 6\end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        1 \\
+        -1 \\
+        -3\end{array}\right]$
+
+    d. $A=\left[ \begin{array}{ccc}
+        1 & 3 & -5 \\
+        1 & 4 & -8 \\
+        -3 & -7 & 9\end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        1 \\
+        -1 \\
+        -3\end{array}\right]$
+
+    d. $A=\left[ \begin{array}{ccc}
+        1 & 2 & -1 \\
+        2 & 2 & 2 \\
+        1 & -1 & 2\end{array} \right]
+        b=
+        \left[\begin{array}{c} 
+        2 \\
+        12 \\
+        5\end{array}\right]$
+
+2. Calculate the determinant of A from 1a-g.