LINEAR ALGEBRA (Math 211)
HW #6 (Due Mon. Oct. 4 )

1. Prove         $\det(A\cdot B) = \det A \cdot \det B$         for $2\times2$ matrices A and B.


2. Compute the signs of following permutations

(a) (5, 2, 4, 1, 3)         (b) (5, 2, 1, 3, 4)          (c) (3, 4, 1, 5, 2)


3. (a) Compute the product $(4, 1, 3, 5, 2)\cdot(3, 2, 5, 4, 1)$

(b) Find the inverse permutation to (4, 1, 3, 5, 2)



Find the following determinants.

4. $\left\vert\begin{array}{rrrrr} a_{11}&0&0&\dots&0\\ a_{21}&a_{22}&0&\dots&0\\ ... ...\vdots&\dots&\vdots\\ a_{n1}&a_{n2}&a_{n3}&\dots&a_{nn} \end{array}\right\vert$ 5. $\left\vert\begin{array}{rrrrr} a_{11}&a_{12}&a_{13}&a_{14}&a_{15}\\ a_{21}&a_{... ...{32}&0&0&0\\ a_{41}&a_{42}&0&0&0\\ a_{51}&a_{52}&0&0&0 \end{array}\right\vert$