Hi,
My linear algebra exam is soon.
Can anyone suggest some study tips ?
Hello,
We covered solving linear systems,vector space,subspace,linear comb and span,linear dep and indep,lagrange poly,eigenvecval,linear recurrence relation,differential equations..
these are the main ones.
thanks for the reply
I'd recommend you know how to row-reduce any matrix and also know how to check whether a system has infinitely many, one, or no solutions.
I'd also memorize how to find an inverse easily whether its by Cramers methd, Gaussian elimination, or LU decomposition. If you only need one method then great.
You need to understand determinants obviously and applications for inverses, eigen-decomposition and linear independence.
Memorize the vector space axioms and sub-space axioms and the definition of linear independence (av1 + bv2 = 0 implies a = 0 and b = 0 for linear independence).
Once you do the above, tie all the bits together. For example use row reduction to get span and dimension for linear systems and use results to calculate all the stuff for solving homogenous linear DE's and recurrence relations.
Also (and this might seem stupid) make sure you remember the right way to multiply two matrices. This can happen (I say this from personal experience) in that if you haven't done it for a while you forget. The easiest way is that you operate on the row in the first matrix and the column in the second.
Also it might help if you are familiar with the applications like with geometry and linear systems. Also if you study inner product spaces, make sure you know the axioms, projections, and how to construct a basis for a space.
You might need to know about rank and nullity of a matrix and how those relate to the above concepts (like span). You also might need to know about rotation matrices and change of basis.
It's hard to give advice without knowing the structure and content of the course, but hopefully the above should provide some useful things to look at.
For any math class, the best way to study for an exam is to use your homework papers. Go over every problem until you are sure you completely understand how to do the problem (which is different from just being able to do the problem). Most teachers do not assign every problem in the book. Once you are clear how to do those problems that were assigned, try some that were not assigned.
For a final exam, include problems from class tests.