Ohhhhhohoh.
n(n+1)/2. I get it now. Thank you for your help! I also realized this could be derived by looking at the triangles as half a square, and since the number of dots in a square in n^2, The number in a triangle is (n^2)/2, + n/2 to account for the dots that are cut in half when the...
Homework Statement
Its a series of triangles, the data table being
n-#
1-1
2-3
3-6
4-10
5-15
I need a general equation in terms of n.
Homework Equations
The Attempt at a Solution
I can't really find anything. The solution has to be non-recursive, and i can find a bunch of...
Homework Statement
Find y as a function of x if
y'''−11y''+28y'=0 y(0)=1 y'(0)=7 y''(0)=2
I have one attempt left on this question. Could someone verify my answer for me?
Homework Equations
The Attempt at a Solution
(use t as lamda)
t^3-11t^2+28t=0...
Homework Statement
Solve the following equation for Z, find all solutions.
z2 -2z + i = 0
Homework Equations
[-b(+/-) sqrt(b2-4ac)]/2a
The Attempt at a Solution
Using the equation above,
z = [2 (+/-) sqrt( (-2)2 - 4 (1) (i)) ]/ 2(1)
=[2 (+/-) sqrt ( 4 - 4i)]/2
=...
Oh, I just got it.
x = -2t
y = s, not 0
and z = t
which means that the vector would be:
(-2t , s, t)T = (-2t, 0, t)T + ( 0, s, 0)T
which gives the bases
(-2, 0, 1)T, and (0, 1, 0)T
Because the equation was
x +2z = 0 or
1x + 0y +2z = 0
y is nonexistent in this case. I assumed that would mean it would be equal to 0 in the basis, but like I said, I wasn't sure if I had calculated the basis correctly. How would I find a value for y?
I also thought that there should be only one basis, but the question asks for 2, and my prof confirmed this. I still don't understand how this would work though.
My work:
x+2z=0
2z = -x
z = - x/2
So if I set x with the parameter t,
x=t
y=0
and z = -t/2, or (-1/2) t
Sorry I...
Homework Statement
The matrix A=
2 0 4
-2 0 -4
-1 0 -2
has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.
Eigenvalue =
Basis ( , , )T , ( , , )T
Homework Equations
The Attempt at a Solution
I have found the...