Homework Statement
dy/dt=y((3t^2)-1), y(1)=-2
Homework Equations
Basic integrals
The Attempt at a Solution
integrate on both sides: dy/y=dt((3t^2)-1)
========>ln(y)=(t^3)-t+c
========>y=e^((t^3)-t+c)
========>y=e^((t^3)-t)e^(c)
I am not sure if its some e rule that I forgot...
Homework Statement
It would help if you guys had access to Maple
Anyways here is the problem: http://poibella.org/calc3f11/wp-content/uploads/2011/09/lab_3_vector_calc_F_11.pdf
It is on question 12 asking for flux and the questions after that.
Homework Equations
In the link
The...
Homework Statement
A 3x3 matrix with all 9 of the numbers being .3
Find all the eigenvalues.
Homework Equations
The Attempt at a Solution
I worked through it and I ended up with (l=lamda) l^3-.9l^2+.54l-.162=0
With my calculator I found one of the values, which means that there...
Can you explain to me how d=a, since a+d=0?
Also since I am actually having a hard time learning this on my own, can you tell me what you mean by "elements" and "linear sum"?
Homework Statement
Find a basis for each of the spaces and determine its dimension:
The space of all matrices A=[a b, c d] (2x2 matrix) in R^(2x2) such that a+d=0
Homework Equations
The Attempt at a Solution
So I jumped at this question without knowing too much about spaces and...
Homework Statement
There are two questions in my problem set that are giving me a hard time:
1. The cross product of two vectors in R^3 is defined by [a1, a2, a3]X[b1, b2, b3]=[a2b3-a3b2, a3b1-a1b3, a1b2-a2b1] (they are all one column) Consider an arbitrary vector v in R^3. Is the...
Homework Statement
Consider a linear system of four equations with three unknowns. We are told that the system has a unique solution. What does the rref of the co efficient matrix look like?
Homework Equations
The Attempt at a Solution
When it says "unique solution" I'm going to...
Every leading coefficient is 1 and is the only nonzero entry in its column.
From the looks of it, it looks like it follows those properties, but I'm just confused if it is still rref if everything is 0, since it doesn't have a leading 1.
According to wikipedia, it is:
In linear algebra a matrix is in row echelon form if
* All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes, and
* The leading coefficient (the first nonzero number from the left, also called the pivot) of a...
Cool, I didn't know that the rref form doesn't need to have straight diagonal "1"s.
As for the solution, would it simply be:
a+2b+e-f=0
c-e+f=1
d+2e-f=2?
Homework Statement
Find all solutions using Gauss-Jordan elimination:
[ 0 0 0 1 2 -1 l 2
1 2 0 0 1 -1 l 0
1 2 2 0 -1 1 l 2]
Homework Equations
Switching rows,
able to scale any row
able to add non zero multiple to row
The Attempt at a Solution
What I did was...