From 8c348f8a1fb6472f63164badd3731240a70f9acc Mon Sep 17 00:00:00 2001
From: JJones780 <2329541+JJones780@users.noreply.github.com>
Date: Thu, 23 May 2024 08:46:20 -0600
Subject: [PATCH] Linear Algebra: Chapter 5 - 3D Linear Transformations -
 Straightforward example to puzzle (#424)

* Update index.mdx

A more applicable example in the final puzzle introducing non-square matrices. The new example is also better related to the puzzle question.
Also caught a few typos -  hopefully didn't introduce any.

* Update index.mdx

fixed indices of matrices from ij,ik,... to 1,2,...

* Update index.mdx

changed example back to original,
modified typo fix as suggested.
---
 public/content/lessons/2016/3d-transformations/index.mdx | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/public/content/lessons/2016/3d-transformations/index.mdx b/public/content/lessons/2016/3d-transformations/index.mdx
index f4ff654d..8c3d29c5 100644
--- a/public/content/lessons/2016/3d-transformations/index.mdx
+++ b/public/content/lessons/2016/3d-transformations/index.mdx
@@ -378,7 +378,7 @@ Here's another puzzle for you: It's also meaningful to talk about a linear trans
 
 A simple example from 3d to 2d would be the shadow cast by a 3d object onto a 2d plane. Although, in order for the transformation to be linear, the light rays should be considered parallel to eachother to simplify the problem. If you consider the light source to be something really far away, like the sun, then this is a reasonable choice to make.
 
-You can represent these transformations with matrices. The number of columns corresponds to the dimension of the input and the number of rows corresponds to the dimension of the output. For example, a matrix that maps coordinates on a sphere to a plane would have three columns and two rows.
+You can represent these transformations with matrices. The number of columns corresponds to the dimension of the input and the number of rows corresponds to the dimension of the output. For example, a matrix that maps coordinates in 3d to 2d would have three columns and two rows.
 
 $$
 A = \left[\begin{array}{ccc}
@@ -387,7 +387,7 @@ a_4 & a_5 & a_6
 \end{array}\right]
 $$
 
-It's meaningful to talk about multiplying these matrices when the number of columns on the left matrix is equal to the number of rows on the right matrix. That whey when apply these matrices to a vector, reading right to left, the dimensions of the input and output match up.
+It's meaningful to talk about multiplying these matrices when the number of columns on the left matrix is equal to the number of rows on the right matrix. That way, when we apply these matrices to a vector, reading right to left, the dimensions of the input and output are as we expect.
 
 $$
 \left[\begin{array}{cc}