Checklist for Midterm
Andrei Jorza
October 26, 2009
The purpose of this checklist is to give you a brief overview of what happened in class until now and
what kinds of things you might expect for the midterm.
1
Up to Quiz 1
1.1
Vectors
1. Representation as (
x
1
,...,x
n
) and the standard basis.
2. Vector operations (+,
−
, scalar multiplication).
3. Inner (dot) product and length.
4. Angles.
5. Vector inequalities (Cauchy-Schwarz and the triangle inequality).
6. When two vectors are perpendicular.
7. Unit vectors and how to make a vector into a unit vector (renormalization).
8. Orthogonal projections of one vector on another.
9. Decomposition of a vector as a linear combination of two other vectors.
1.2
Matrices and Determinants
1. What matrices are and how to add, subtract and multiply them.
2. Determinants 2x2 and 3x3 and how to compute them.
3. Properties of the determinant (swap two rows etc).
4. The cross product geometrically and the determinant definition.
5. Properties of the cross product and the fact that the length represents the area of the parallelogram.
6. Geometrical interpretation of the determinant as area and volume.
7. Equation of planes through a point and perpendicular to a normal vector.
8. Equation of planes through a point and perpendicular to a line (given by equation).
9. Equation of planes through 3 points (compute the normal vector as cross product).
10. Distance from point to plane.
1

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
11. General matrices nxn.
12. General determinants and how to compute them recursively with the line expansion formula.
13. Inverse of a matrix, what it is and that it exists when the determinant does not vanish.

This is the end of the preview.
Sign up
to
access the rest of the document.