its definiely true: eigenvalues don't change under row operations. If you have a diagonal matrix, you can check the entries are eigenvalues by pairing them with standard basis vectors as the eigen vectors.
4 rows and 6 columns: Like hypnotik said: a matrix of all zeros has rank 0 due to all 4 rows being 0 and has nullity 6 due to all columns being zero.
The zero matrix will be the only matrix that satisfies this condition. If you have one nonzero entry the rank becomes 1 and nullity becomes 5.
Just define the function piece-wise using the greatest integer function |_x_|:
Let f(x)=x-|_x_| if |_x_| is even
and
f(x) = 1-x+|_x_| if |_x_| is odd
This fucntion will just be the lines y=x and y=1-x on [0,1] repeated over and over.
Your right, in that i doesn't have to be expensive. A couple kegs at a private residence is not expensive. However, if you're venue requires you to hire professional bar tenders and you serve mix drinks, the tab adds up quickly. I've even seen places that require your hire security if you...
if you have good relationships with previous landlords, you can ask them to write you a recommendation. Sometimes a good word from another property manager can give you the edge.
I remember this. I also remember the match where they broke up. They were taking on the Twin Towers when Hogan left Macho man by himself in ring to get help for their lady manager after she was hurt. Macho man single handedly defeated the Twin Towers but felt betrayed by Hogan. Oh the drama!!!
Marketing owned me when V-8 fusion came out. I was like "whoa that bottle looks cool! I'm getting some". However, I actually like V-8 fusion now so I guess its a win-win situation.
the expression x(dz/dx)+y(dz/dy) is exactly zero.
proof:
Let u=y/x
By the chain rule, we have dz/dx=f'(u)*(-y/x^2) and dz/dy=f'(u)*(1/x).
The terms in the expression above then cancel.
the saying "its not what you know, but who you know" goes a long way when it comes to getting your first intership/job. Networking with friends of my parents is how I got my first real job.
Next time, how about you throw the party and invite only people you're comfortable with. I find that if I already know more than half the people at a party I have a much better time.
people sweat more in joint areas due to skin on skin action. Hence we wear undershirts and underwear to protect our external clothes from smelliness. It's easier to wash 5 boxers and undershirts than 5 collar shirts and pants.
I've seen women wear protective googles some times. Men typically toss the ball much faster than women.
If women aren't getting injured, why load oneself down with unnecessary gear.
washing my hands has nothing to do with my genetics. They were passed to me from my parents and don't change through out my life. All I'm saying is that modern medicine probably won't have a major impact on human evolution in the short run.
I do agree that living in a sterile environment...
given the rate that humans reproduce, I highly doubt you can measure any significant genetic improvements or regression in our population over the past 500 years or since modern medicine has taken hold.
I also highly doubt there will be any significant difference in the next 500 years...
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