# We have to solve the following equation (the matix in the document). How am i meant to figure out what a=? when i have a cube? i have done some working but i am not sure what ot do next. the...

We have to solve the following equation (the matix in the document).

How am i meant to figure out what a=? when i have a cube?

i have done some working but i am not sure what ot do next.

the answer says --> 0,1,2

i got 1 and 2 by just using a[(a^2 -3a +2)]

i don't know what to do with the a in the front (A^3)

hope this makes sense :)

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### 2 Answers

You found teh determinant to be `a^3-3a^2+2a` , and since the matrix is singular the determinant is zero.

So `a^3-3a^2+2a=0`

`a(a^2-3a+2)=0`

`a(a-2)(a-1)=0`

By the zero product property at least one of the **three** factors must be zero. Set each factor equal to zero:

a=0

a-2=0 ==> a=2

a-1=0 ==> a=1

So the solutions are a=0,1, or 2.

that makes sense, thank you :)