What is the determinant of a matrix with a variable?

[TW Cantor]

Homework Statement

The matrix A is given as:
[25 , 5]
[-150 , -30]

find, in terms of m, the expression det(A-mI). This will be in a quadratic expression in m.

Homework Equations

det(A) = ad-bc

The Attempt at a Solution

i have no idea how to approach this but i worked out the det(A) using the equation above to be 0. This makes this matrix singular. I don't understand what the I and the m are representing

 

[icystrike]

I= [1,0]
[0,1]

mI= [m,0]
[0,m]

Can u combine A-mI into a single 2 by 2 matrix?
(With that u can find the determinant like how u always do)

 

[TW Cantor]

ahhh yes i get it now. if i do A-mI and then calculate the determinant of that new matrix then i get: m² + 5m.

thanks a lot :-)