00:01
Hello, so here we let a be any 2x2 -matrix, a, b, c, d, and we have that the v vector is a vector 2 -3 is going to be an eigenvector associated with the eigenvalue lambda being negative 1.
00:14
So then by definition of the eigenvector, we have that a times v is equal to lambda times v, so we have a, b, c, d times the vector 2, 3 is equal to negative 1 times the column vector 2 -3.
00:26
So that is then going to give us 2a plus 3b and then 2c plus 3d is going to be equal to the column vector here at negative 2, negative 3.
00:51
And then by the equality of the matrices, we have 2a plus 3b is equal to negative 2, and then 2c plus 3d is equal to negative 3.
01:01
So then we can go ahead and solve the equations.
01:03
Hello...