### gainfully employed

grading linear algebra again.

so far this quarter, i’ve (1) returned

the text from last quarter (late) and

i’ve (2) gone back and got a different

copy of the same text a week later.

and that’s it… a week and two days

into the semester.

but starting today there’ll be bigfat

envelopes full of homework piling up

in my mailbox. so very likely i’ll be

posting less over in the cooking show

(where i’ve had a pretty good run going

for about a week).

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September 8, 2014 at 12:14 pm

3. Mark each statement True or False.

You will receive full credit for each correctly marked True statement; however each False statement must also include a counter-example for full credit.

i. Foranytwo3-vectorsuandv,u·v=v·u

ii. Foranytwo3-vectorsuandv,u×v=v×u

iii. Every product of elementary matrices is an elementary matrix.

iv. Every product of elementary matrices is an invertible matrix.

v. If A and B are invertible 2-by-2 matrices, then AB is invertible.

vi. If A and B are invertible 2-by-2 matrices, then A+B is invertible.

vii. Every symmetric matrix is invertible.

viii Every invertible matrix is symmetric.

ix Every system of two equations in two variables has at least one solution.

x Every system of two equations in two variables has at most one solution.