The ones that can be converted unto a higher order differential equation, single one what does it mean if there is at least one f(t) that is nonzero? How do you check is the solutions to the matrix equation are linearly independent? How is the wronskian for the solution vectors different from previous use of wronskian? What type of systems are we focusing on here?

What type of systems are we focusing on here?

The condition is that the highest order derivative needs to be able to be written in terms of components of the dependent, independent variables and their lower order derivatives What's condition for a system to be able to be converted into a single linear differential equation? What does the wronskian have to equal for all t values to be linearly independent? What is the term f(t) in the system represent? Consider the principle of superposition for corresponding homogenous equation

What's condition for a system to be able to be converted into a single linear differential equation?

To be able to use them to solve first order systems How do you check is the solutions to the matrix equation are linearly independent? What does the solution vector function satisfy? What's the focus with matrices for? Consider the principle of superposition for corresponding homogenous equation

What's the focus with matrices for?

Matrices of functions, where each cell is a funtion How do you check is the solutions to the matrix equation are linearly independent? What type of matrices can be used to express a system as? Consider the principle of superposition for corresponding homogenous equation For homogenous equation matrix, what happens to the linear combination of the solutions if they are all linearly independent?

What type of matrices can be used to express a system as?

When all the functions in its entry can be differentiated or integrated How do you solve a non homo matrix equation? What does the solution vector function satisfy? When is a function matrix differentiable or integrable? What's condition for a system to be able to be converted into a single linear differential equation?

When is a function matrix differentiable or integrable?

By deriving each of its entries What's the focus with matrices for? What is the column vector f(t) full of? How do you find the derivative of a function matrix? What type of matrices can be used to express a system as?

How do you find the derivative of a function matrix?

It's a x prime = p_11(t)x_1 + ... + p_1n(t)x_n + f_1(t) What does the system we are converting look like? What's the focus with matrices for? What does the solution vector function satisfy? How is the wronskian for the solution vectors different from previous use of wronskian?

What does the system we are converting look like?

It represents the hon-homogenous part of the equation What is the term f(t) in the system represent? How is the wronskian for the solution vectors different from previous use of wronskian? What is the solution like? What's the focus with matrices for?

What is the term f(t) in the system represent?

X prime = P(t) x + F(t) What is the solution like? What type of matrices can be used to express a system as? what does it mean if there is at least one f(t) that is nonzero? What does the Matrix differential equation that is equivalent to that system look like?

What does the Matrix differential equation that is equivalent to that system look like?

It's made of column vectors for X and X prime and f(t) and a full matrix with p(t) what does it mean if there is at least one f(t) that is nonzero? How do you solve a non homo matrix equation? What's the focus with matrices for? What is the matrix differential equation made of?

What is the matrix differential equation made of?

Matrix Diff Eq System (Math 81 M6)

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Calculus - Geometry

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The ones that can be converted unto a higher order differential equation, single one

The condition is that the highest order derivative needs to be able to be written in terms of components of the dependent, independent variables and their lower order derivatives

To be able to use them to solve first order systems

Matrices of functions, where each cell is a funtion

When all the functions in its entry can be differentiated or integrated

By deriving each of its entries

It's a x prime = p_11(t)x_1 + ... + p_1n(t)x_n + f_1(t)

It represents the hon-homogenous part of the equation

X prime = P(t) x + F(t)

It's made of column vectors for X and X prime and f(t) and a full matrix with p(t)

X - this contains all the x_1(t) and x_2(t) in the system X prime - contains all the first order derivatives of the system

It's made of all the coefficient functions

It's full of the non homo parts of the system

It means the whole system is non-homogenous

The solution is a vector function

It satisfies the first order system

Its when if the solutions for the matrix diff equation has constant coefficients c_1,c_2 then the linear combination of all the solutions results in a vector x(t) that is also a solution to the matrix equation.

That linear combination off all solutions is a general solution to the matrix equation

Use the wronskian where its W = det of |( matrix of solution vectors )|

Before the wronskian consisted of all derivatives of previous row's entry, here thats not the case

It has to equal zero for all the solution vectors to be linearly independent

X prime = p(t)X + f(t)

F(t)

You solve it using the method we already know in solve higher order differential no homo equations where we use complimentary solutions and particular solutions, X(t) = x_c(t) + x_p(t) Where x_c(t) is general solution of corresponding homo equation X_p(t) is a particular solution for the non homo equation

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Matrix Diff Eq System (Math 81 M6)

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