MATH 253 Fall 2015
Matrix Algebra
Test 1 Info and Review Sheet
Test 1 is Wednesday, October 7 in class (8:15-9:05). It covers 1.1-1.3. All
questions are written answer, the total test is out of 20. You can use a
calculator. The best way to study is to do practice problems- so the
sample questions listed on the website. The book also has really good
chapter summaries at the end of each chapter.
The main things you need to know:
 Operations on vectors: sum and difference
 Scalar multiplication (useful for midpoints and unit vectors)
 Length of vectors
 Distance between vectors
 Dot products and how they are useful (finding angles, doing
projections)
 Cross products and how they are useful (finding perpendicular
vectors, areas of parallelograms and triangles)
 Orthogonality
 Lines in 3D space: point-parallel form, two-point form, using
parametric equations
 Planes in 3D space: point-normal form, standard form, using three
points, parametric form
 Finding intersection of line and plane
 How to tell if 2 lines are parallel, intersect or are the same
 How to tell if 2 lines are parallel, intersect or are the same
 Distance from point to plane (don’t memorize formula, it would be
given to you if needed)
Theorem Info:
In general you should be familiar with theorems we saw in class in that you
can apply them to specific questions.