How to Study for an Algebra Test on Vectors and Matrices?

[CGUE]

If you could offer any tips for studying for an Algebra test for tomorrow morning it would be great.
It covers:

Vectors:

• Vector quantities and $\mathbb{R^n}$
• $\mathbb{R^2}$ and analytic geometry
• Points, line segments and lines. Parametric vector equations. Parallel lines.
• Planes. Linear combinations and the span of two vectors. Planes though the origin.
• Parametric vector equations for planes in $\mathbb{R^n}$. The linear equation form of a plane.

Matrices:

• Introduction to systems of linear equations. Solution of 2 × 2 and 2 × 3 systems and geometrical interpretations.
• Matrix notation. Elementary row operations.
• Solving systems of equations via Gaussian elimination.
• Deducing solubility from row-echelon form. Solving systems with indeterminate right
  hand side.
• General properties of solutions to Ax = b.
• Matrix operations.

No calculators are allowed and it goes for 20 minutes.

 

[mathwonk]

tip: if the test is tomorrow morning, all studying should be pretty much completed before tonight. only mild review should be appropriate.

i say this now that the test is over so as not to upset you before the test, but to help on the next test.

 

[CGUE]

tip: if the test is tomorrow morning, all studying should be pretty much completed before tonight. only mild review should be appropriate.

i say this now that the test is over so as not to upset you before the test, but to help on the next test.

Hmm yeah I got the harder paper and when I solved for the intersection between two planes I was lost when I got infinite solutions after using Gaussian Elimination.

And I still couldn't grasp the concept of linear combination of vectors, i.e. I haven't found a mechanical way to solve questions like these.

Well I guess it all really counts in the end since my final exam is worth 64% of the entire assessment over the semester.

 

[mathwonk]

of course one should expect two planes to intersect in a line, i.e. infinitely many points.

try to think geometrically.