how do i prove the following is a theorem in SD
[(A -> B)->A]->A
... i started off by assuming [(A -> B)->A] then assume ~A to try to derive A in the end... but now I'm stuck :(
and also:
Suppose we dropped from SD the rule for vE, and adopted in its place the rule of Disjunctive...
any ideas on number four?
i don't know how to prove A^2 cannot = -I for 5x5 matrices.. i know it's possible for 2x2 so why would it be different for a 5x5?
i know dick mentioned something about determinants but finding a determinant of a 5x5 would mean 25 different variables? .. is that the...
i found a counter example by setting
a^2 + bc + 1 = 0
d^2 + bc + 1 = 0
b (a + d) = 0
c (a + d) = 0
where a and d are negatives of each other and bc = neg (a^2) minus one
thanks :)
thanks everyone for your input it really helped me out..
for one i have A= I or 2I but if A=2I then A-2I is not invertible so the statement is false
for two i don't really understand Jbunniii's hint.. i originally thought A equaled 4I and 3I but when i put these back into the original A^2 -...
hey in response to your message hurkyl, I'm taking "elementary linear algebra"
and right now we have covered basic matrix stuff like inverse, determinants, solving systems of linear equations, multiplying/adding matrices etc..
i think these questions relate to chapter two which is about...
hey guys thanks for your help.. so far for one i have
A = I then A-2I is invertible so the statement is true.
for two i have
A = 3I or A = 4I but neither of these work when i plug it back into the original equation?
the last two are real matrices..
for four I'm trying to prove that A^2 can not =...
I have no idea how to approach these.. any help would be greatly appreciated.
I can't seem to find this in the book either so if there are any links on the web that relate to these questions please let me know.. Thanks!
Prove or disprove the following statements. I and 0 represent the...