diff --git a/source/linear-algebra/source/04-MX/03.ptx b/source/linear-algebra/source/04-MX/03.ptx
index 582acd20e..ce5a873ea 100644
--- a/source/linear-algebra/source/04-MX/03.ptx
+++ b/source/linear-algebra/source/04-MX/03.ptx
@@ -79,7 +79,7 @@
x_2\begin{bmatrix}1\\-1\\1\end{bmatrix}+
x_3\begin{bmatrix}0\\1\\1\end{bmatrix}
-
+
Zero
At most one
Exactly one
@@ -103,7 +103,7 @@
If \vec x=\left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right]
and B = \left[\begin{array}{ccc}\vec b_1& \vec b_2&\vec b_3\end{array}\right]=\left[\begin{array}{ccc}1&1&0\\0&-1&1\\1&1&1\end{array}\right],
which of these matrix equations can be used to find x_1,x_2,x_3?
-
+
\vec v=B\vec x
B\vec v=\vec x
\vec v=B^{-1}\vec x
diff --git a/source/linear-algebra/source/future-ON/01.ptx b/source/linear-algebra/source/future-ON/01.ptx
index cd5c34969..8528f87ee 100644
--- a/source/linear-algebra/source/future-ON/01.ptx
+++ b/source/linear-algebra/source/future-ON/01.ptx
@@ -23,7 +23,7 @@
Let \vec v =\left[\begin{array}{c} 1 \\ -1 \\ 0 \\ 2 \\ 3 \end{array}\right] and \vec w=\left[\begin{array}{c} 5 \\ 12 \\ -1 \\ 1 \\ 2 \end{array}\right]. What is \vec v \circledast \vec w?
-
+
- 25
- \left[\begin{array}{c} 5 \\ -12 \\ 0 \\ 2 \\ 6 \end{array}\right]
- 1