I think you should take a look in other text of linear algebra also, as a complement. I know the MIT professor is very good, but seeing some things from different points of view also helps. Also you should practice solving problems.
I've been working with Linear Algebra Done Right by Sheldon...
If you know the coordinates of the vector F in any basis, let's say \{e_i\} ,
F=g_1e_1+...+g_ne_n
Then you can use a matrix to find the coordinates in other basis \{b_{i}\}:
[F]_b stands for the column matrix of coordinates from the vector F in the \{b_{i}\} basis. Is easy to show that...
Re: I need help urgently asap proving that -0=0
Another:
Let be x de inverse additive of 0 (that is -0), then by definition:
0+x=0
Since 0 is the additive identity:
x=0
Well, there exist a lot of theorical reason for why r^2, must be 2 and no 2.00031415..., one example is dimentional analysis. What does (meter)^2.000123... mean?
But as far as we are dealing with reality, we cannot prove things like mathematical proofs, and even nature can behave weird, and...
Well, r^2 actually could be r^2.00000123... , we don't know, until we taste it with experiments. But then, 2 is very accurate. When we do models and theories we must be aware that our models might be not fully exact, but if these give some good results, and are accurate within their own range of...
Why do you think that there are more women in chemistry than engineering or even physics? At least in my University in math and chemistry there is more female students than male.
I was thinking that in chemistry it is because existed a great influence that maybe could change the point of...
But how about the Floyd Rose bridge? http://en.wikipedia.org/wiki/Floyd_Rose
When you put the string, it doesn't need to wind loops to hold the strings, they hold due to the pressure that exerts the screw. And in the other end of the string also are holding with a screw near the nut. But...
I don't say that they are synonymous. Using this theory can be demonstrated rigorously many manipulations in which are used differentials.
I named it 'cheating form' because many times it is used without clarify its properties and proof them (for example can I do this? dx/dy=1/f'(x) ). Even...
Actually that is not a differential form, it's only notation. Even it may to be written like this:
\int f = g
Where f = g' and being f and g functions of real variables.
Well, dy=f'(x)dx is a "cheating" form. However it's used to simplify the things and make them more intuitive (and...
Yes, since the two springs have the same stiffnes and the same unstretched lengths, when you apply them a force, they stretched to the same length. Therefore they form an isoceles triangle.
Check out this program: http://www.xente.mundo-r.com/explora/ondas/ondas.zip
It let you to simulate waves and pulses. Install and open and then click "pulses in one dimension".
In pulse 2 in Height option, put -1. And select "opposite directions". Click "Draw", control the speed, and...