User 1123581321

Let V be the set of all 4x4 singular matrices A (singular means detA=0)

Is V closed under scalar multiplication? explain.

is V closed under addition? explain.

Is V a subspace of the vector space M_4x4 (underscore indicates 'sub') of all 4x4 matricies? explain.

Why do i ask such a question? Well I've not taken linalg in 6 years, and I'm attempting to help a sibling who is taking it right now. Thanks in advance for your answers and explanations, hopefully they will jog my memory enough so I can be of assistance.

My guesses:

closed under scalar multiplication because the scalar would factor out in solving for a det, therefore a singular matrix multiplied by a scalar would always return a singular matrix.

addition, not closed because addition of a term to all entries in a matrix will clearly result in a matrix that is not singular for the same reason that (A*B)+4 does not equal (A+4)*(B+4)

not sure on the third part, i would guess yes, because there are more 4x4 matricies than there are 4x4 singular matricies, or perhaps there are just infinite of both....

thanks again for your answers

T:F->R, T(x)= ∫[0,1] x'(t)/(t^2+1) dt

T:F->R, T(x)= ∫[0,1] t/(x(t)+100) dt

P:F->F, P(x) = 2x''(t)+tx'(t)

Its been a while (4 years) since i took linear algebra and i'm trying to remember how to do some of this. Thank you for the answers, explanation is very much appreciated!

Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, with an enrollment of 300 students, a study found that 50 students smoked at least one pack of cigarettes a day. at 'alpha'=0.05, test the claim that 18% of all high school students smoke at least one pack of cigarettes a day. use the P-value method.

it has been found that 85.6% of all enrolled college and university students in the United States are undergraduates. A random sample of 500 enrolled college students in a particular state revealed that 420 of them were undergraduates. Is there sufficient evidence to conclude that the proportion differs from the national average? Use 'alpha'=0.05.

It has been reported that 40% of the adult population participate in computer hobbies during their leisure time. A random sample of 180 adults found 65 engaged in computer hobbies. At 'alpha'=0.01, is there sufficient evidence to conclude that the proportion differs from 40%?

so, im not entirely sure what happened. heres the situation, all of my computers icons to all the programs have stopped working and their icons have changed. every time i click one of them i get the message ...is not a valid win32 application. i can go and manually search for the program on my c drive, but obviously this will not do. i need to get my pc fixed. if anyone has any idea how to fix this w/o the use of restore points, i would appreciate it.

Im currently working toward my degree in Mechanical Engineering. I would just like to hear of some personal experiences, or opinions on what ME jobs are the best. Im not looking for top pay, that can be found on google, I want personal opinion with a little support for your ideas.

Lets say you drop a ball from a rooftop. The laws of physics say that the ball will fall with an acceleration of 9.91m/s^2. So every time you drop that ball, it will fall almost exactly the same way. Another example, lets say you have a simple electric circuit. In that circuit, it is possible to find current, voltage, resistance, and many other aspects of that circuit at all the different nodes and resistors, and whatever you happen to have in that circuit. So here is the question, since the human brain also runs on electric signals of some kind, what is the force, or ability, that the human brain has that is able to give someone the ability to make a decision. Shouldn't that decision be based on the laws of physics applied to the human mind in ways more complex than are currently known? Is what we as humans call choice merely an Illusion?

Just food for thought that's all. 10 pts for the best argument/answer.