diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx
index 8604e89d3..3b8a8d088 100644
--- a/source/linear-algebra/source/02-EV/05.ptx
+++ b/source/linear-algebra/source/02-EV/05.ptx
@@ -268,6 +268,7 @@ In particular, the standard basis for \mathbb R^3 is \{\vec e_1,\vec e
+
\left\{
@@ -300,8 +301,24 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea
+
+
+A.
+All pivot rows and columns: \left[\begin{array}{cccc}
+1 & 0 & 0 & 0 \\
+0 & 1 & 0 & 0 \\
+0 & 0 & 1 & 0 \\
+0 & 0 & 0 & 1
+\end{array}\right] \sim \left[\begin{array}{cccc}
+1 & 0 & 0 & 0 \\
+0 & 1 & 0 & 0 \\
+0 & 0 & 1 & 0 \\
+0 & 0 & 0 & 1
+\end{array}\right]
+
+
\left\{
@@ -334,8 +351,24 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea
+
+
+D.
+Both a non-pivot row and non-pivot column: \left[\begin{array}{cccc}
+2 & 2 & 4 & -3 \\
+3 & 0 & 3 & 0 \\
+0 & 0 & 0 & 1 \\
+-1 & 3 & 2 & 3
+\end{array}\right] \sim \left[\begin{array}{cccc}
+1 & 0 & 1 & 0 \\
+0 & 1 & 1 & 0 \\
+0 & 0 & 0 & 1 \\
+0 & 0 & 0 & 0
+\end{array}\right]
+
+
\left\{
@@ -369,8 +402,24 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea
+
+
+D.
+Both a non-pivot row and non-pivot column\left[\begin{array}{rrrrr}
+2 & 2 & 3 & -1 & 4 \\
+3 & 0 & 13 & 10 & 3 \\
+0 & 0 & 7 & 7 & 0 \\
+-1 & 3 & 16 & 14 & 2
+\end{array}\right] \sim \left[\begin{array}{rrrrr}
+1 & 0 & 0 & -1 & 1 \\
+0 & 1 & 0 & -1 & 1 \\
+0 & 0 & 1 & 1 & 0 \\
+0 & 0 & 0 & 0 & 0
+\end{array}\right]
+
+
\left\{
@@ -403,8 +452,24 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea
+
+
+A.
+All pivot rows and columns: \left[\begin{array}{cccc}
+2 & 4 & -3 & 3 \\
+3 & 3 & 0 & 6 \\
+0 & 0 & 1 & 1 \\
+-1 & 2 & 3 & 5
+\end{array}\right] \sim \left[\begin{array}{cccc}
+1 & 0 & 0 & 0 \\
+0 & 1 & 0 & 0 \\
+0 & 0 & 1 & 0 \\
+0 & 0 & 0 & 1
+\end{array}\right]
+
+
\left\{
@@ -436,6 +501,21 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea
+
+
+C.
+All pivot columns, but a non-pivot row: \left[\begin{array}{rrr}
+5 & -2 & 4 \\
+3 & 1 & 5 \\
+0 & 0 & 1 \\
+-1 & 3 & 3
+\end{array}\right] \sim \left[\begin{array}{rrr}
+1 & 0 & 0 \\
+0 & 1 & 0 \\
+0 & 0 & 1 \\
+0 & 0 & 0
+\end{array}\right]
+