SOLUTION: |a 1 1 1| |1 a 1 1| |1 1 a 1| =(a+3)(a-1)^3 |1 1 1 a|

Question 1044577: |a 1 1 1|
|1 a 1 1|
|1 1 a 1| =(a+3)(a-1)^3
|1 1 1 a|
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

Perform ERO3's (which do not change the value of the determinant)
, and , giving

.
= ,
by Laplace expansion with the the first column as pivot.
Factoring 1-a from all three rows give
= .
Now , and so the last determinant is equal to
.
Now perform the following ERO3 , and ERO3 IN SUCCESSION, to get
=.
=
By performing Laplace expansion with the first row as pivot.
=.

RELATED QUESTIONS
1/(a^-1/3) (answered by Tatiana_Stebko)

(a - 1)^1/3 =... (answered by mananth)

1/a-1 + 3/3a-1 =... (answered by unreal4evr)

Solve 1/a - 1/6 =... (answered by lynnlo)

1/a -1 / 1/a... (answered by MathLover1)

1-(a-1)/1+(a-1) (answered by stanbon)

1 + 1 -- a ------------------- 1 - 1 -- 2a (answered by stanbon)

A... (answered by colliefan)

abc=1 show that... (answered by Edwin McCravy)