Question

Consider the system of differential equations

[ y₁'=16 y₁-8 y₂; y₂'=20 y₁-8 y₂ ]
a. Rewrite this system as a matrix equation

Answer 1

The system of differential equations is rewritten as a matrix equation by representing the derivatives of y₁ and y₂ as a vector, and the coefficients of y₁ and y₂ as a matrix.

Step-by-step explanation:

To rewrite the system of differential equations as a matrix equation, we start with the given equations:

• y₁' = 16y₁ - 8y₂
• y₂' = 20y₁ - 8y₂

We can represent the derivatives of the functions y₁ and y₂ as a vector:

[ y₁' ]
[ y₂' ]

The corresponding coefficients can be written as a matrix multiplied by the vector of functions:

[ 16 -8 ] [ y₁ ]


[ 20 -8 ] [ y₂ ]

Thus, the matrix equation representing the system is:

[ y₁' ] = [ 16 -8 ] [ y₁ ]


[ y₂' ] [ 20 -8 ] [ y₂ ]