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  1. FUNDAMENTALS OF LINEAR ALGEBRA James B. Carrell carrell@math.ubc.ca (July, 2005)

  2. There are a number of excellent online texts which are available free of charge. Among the best are Linear Algebra [7] by Jim He eron, http://joshua.smcvt.edu/linearalgebra and A First Course in Linear Algebra [2] by Robert A. Beezer, http://linear.ups.edu/download/fcla-electric-2.00.pdf

  3. This booklet contains the worksheets for Math 54, U.C. Berkeley’s linear algebra course. The introduction to each worksheet very briefly motivates the main ideas but is not intended as a substitute for the textbooks or lectures. The questions emphasize qualitative issues and the problems are more computationally intensive.

  4. Linear Algebra Igor Yanovsky, 2005 4 1 Basic Theory 1.1 Linear Maps Lemma. If A 2 Matmxn(F) and B 2 Matnxm(F), then tr(AB) = tr(BA): Proof. Note that the (i;i) entry in AB is Pn P j=1 fiijflji, while (j;j) entry in BA is m i=1 fljifiij. Thus tr(AB) = Xm i=1 Xn j=1 fiijflji; tr(BA) = Xn j=1 Xm i=1 fljifiij: 1.2 Linear Maps as Matrices ...

  5. Linear Algebra Worksheet 2.Although in practice you will not need to do a lot of linear algebra by hand (that’s what computers are for!), you should be able to perform basic computations, and know how to use computational resources like Matlab, Mathematica, Wolfram Alpha to help you debug your code. (a)(3 points) Compute a b c d T e f g h :

  6. Solve linear equations using addition and subtraction. Solve linear equations using multiplication and division. Use linear equations to solve real-life problems.

  7. The interesting thing to say is that the answer is any vector in the nullspace of 1 1 1 1. The simplest solution is 2 6 6 4 0 0 0 0 3 7 7 5. 9A-5 (a) The obvious answer to this question is v = 2 6 6 4 0 0 1 0 3 7 7 5; for any matrix Awith four columns, A 2 6 6 4 0 0 1 0 3 7 7 5is the third column of A. But there are other answers: Remember, the ...

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