Write the linear system of differential equations in matrix form then solve the system.
dx/dt = x + y
dy/dt = 4x + y
x(0) = 1, y(0) = 2

In matrix form, the system is

First find the eigenvalues of the coefficient matrix (call it ).

Find the corresponding eigenvector for each eigenvalue:

Then the system has general solution

or

Given that and , we have

so that the system has particular solution

x = 12

y = 15

step-by-step explanation:

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b