From 303c3d487ddcc4901193f44e9a16156fb129354d Mon Sep 17 00:00:00 2001
From: Siddhanta Mishra <73783282+sidamishra@users.noreply.github.com>
Date: Fri, 20 Mar 2026 22:05:16 -0400
Subject: [PATCH 1/2] fix: present tense

Present tense to be consistent with the rest of the recap.
---
 src/cross.typ | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/cross.typ b/src/cross.typ
index 7a5bc7c..9ecfbd3 100644
--- a/src/cross.typ
+++ b/src/cross.typ
@@ -359,9 +359,9 @@ A brief summary of the last few chapters.
 
 - Both are used in the theory of planes:
   - We use the dot product to show that the normal vector
-    to the plane $a x + b y + c z = d$ was the vector $vec(a,b,c)$.
+    to the plane $a x + b y + c z = d$ is the vector $vec(a,b,c)$.
   - We use the projection from the dot product to find the distance from a point to a plane.
-  - Given three points on a plane, the cross product let us find the normal vector.
+  - Given three points on a plane, the cross product lets us find the normal vector.
 
 See also @table-vector-objects, which summarizes some of the vectors
 we've seen in applications.

From c54d37bbbb44a2a7b82fe10a62134886703dd3ab Mon Sep 17 00:00:00 2001
From: Siddhanta Mishra <73783282+sidamishra@users.noreply.github.com>
Date: Fri, 20 Mar 2026 22:11:32 -0400
Subject: [PATCH 2/2] fix: periods in examples and boldface vector

---
 src/matrix.typ | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/matrix.typ b/src/matrix.typ
index c1d5519..a12b97b 100644
--- a/src/matrix.typ
+++ b/src/matrix.typ
@@ -29,10 +29,10 @@ I wouldn't worry too much about the axioms until later; for now, read the exampl
 #example(title: [Examples of linear transformations])[
   The following are all linear transformations from $RR^2$ to $RR^2$:
 
-  - The constant function where $T(bf(v)) = bf(0)$ for every vector $v$
+  - The constant function where $T(bf(v)) = bf(0)$ for every vector $bf(v)$.
   - Projection onto the $x$-axis: $T(vec(x,y)) = vec(x,0)$.
-  - Rotation by an angle
-  - Reflection across a line
+  - Rotation by an angle.
+  - Reflection across a line.
   - Projection onto the line $y = x$.
   - Multiplication by any $2 times 2$ matrix, e.g. the formula
     $ T(vec(x,y)) = vec(x+2y,3x+4y) $