Determinant with variable?

A = [1-u -1 2]
[0 4-u 3]
[0 4 -u]
Is it possible to get something like
-u^3 +5u^2 -16u +12?

If it's wrong, any help would be appreciated. Thanks!

Question

Determinant with variable?

A = [1-u    -1     2]
       [0       4-u    3]
       [0         4    -u]
Is it possible to get something like 
-u^3 +5u^2 -16u +12?

If it's wrong, any help would be appreciated. Thanks!

anonymous · Answer

(1-u) * [(4-u+u) - (12) ] = 8u - 8

anonymous · Answer

isn't it (4-u)(u)?

tkhunny · Answer

Close.  (4-u)(-u)

anonymous · Answer

opps my bad. Yea you're right

anonymous · Answer

so i did that and ended up with that polynomial of degree 3

anonymous · Answer

(1-u) * [(4-u)(-u) - (12) ] = -u^3+5 u^2+8 u-12. So yes, you're correct

anonymous · Answer

Thanks! also any advice for finding a value of u to make A invertible?

anonymous · Answer

-u^3+5 u^2+8 u-12 ≠ 0 (not equal)
u ≠ -2, 1, 6