Hint: Write the system of equations like this:Jamiey1988 said:I have been asked to write the following two first order equations in matrix form.
x' = y
y' = -x
I also must state that the follow on to the question asks for the only fixed point. The two first order equations came from a modified Van der pol equation.
Jamiey1988 said:Ok would it be correct to write as a jacobian matrix?
If so would this be th answer?
0 1
-1 0
The numbers above are meant to be a matrix, sorry bad formatting:)
Writing two first order equations in matrix form is a way to represent a system of linear equations in a more compact and organized manner. It allows for easier manipulation and solution of the equations, especially when dealing with larger systems.
To convert two first order equations into matrix form, you need to identify the coefficients of each variable in the equations. These coefficients will form the elements of a matrix, with the variables being the corresponding rows or columns. The constants in the equations will form a separate column matrix.
Using matrix form for first order equations allows for easier manipulation and solution of the equations, as well as better visualization of the relationships between variables. It also allows for the use of matrix operations and techniques, which can simplify and speed up the solving process.
Sure, let's say we have the following system of equations:
x + 2y = 5
3x + 4y = 10
Converting this into matrix form would give us:
[1 2] [x] = [5]
[3 4] [y] = [10]
where the left matrix is the coefficient matrix and the right matrix is the constant matrix.
Writing two first order equations in matrix form is an application of linear algebra, specifically matrix operations and techniques. It allows for the use of matrix algebra to solve the equations, which is a fundamental concept in linear algebra.