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!

Answer 1

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

Answer 2

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

Answer 3

Close. (4-u)(-u)

Answer 4

opps my bad. Yea you're right

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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