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[Chony]

For now this is the only problem I dont get:

Find the (3x3) nonsingular matrix A if A² = AB + 2A where B =

[ 2 1 -1 ]
[ 0 3 2 ]
[-1 4 3 ]

 

[Lane_Myer]

i have a BS in math but i dont remember i lose.

 

[Chony]

Come on, there has to be someone who knows how to do this problem? Anyone? My math teacher is retarded and if you get any problems wrong on the homework you get zero points for the assignment, and there are several problems.

 

[sefskillz]

all i can suggest is to make a matrix for a

A =

[ a11 a12 a13 ]
[ a21 a22 a23 ]
[ a31 a32 a33 ]

and carry out the operations with these variables and see what you come up with. i'd do it, but it sounds like a lot of work

 

[Chony]

Well this section is on inverses, any way they would help me here?

 

[Lathentar]

Yeah, you should multiply everything in that equation by A^-1

So you get A^-1 * A * A = A^-1 * A * B + 2 * A^-1 * A

This SHOULD simplfy to
A = B + 2*I, where I is the identity matrix.

So, B = A - 2*I

So B =
[ 0 1 -1 ]
[ 0 1 2 ]
[-1 4 1 ]

EDIT: Always check your work... (I just did using Matlab)

>> A*B + 2*A

ans =

5 1 -3
-2 17 12
-5 23 18

>> A * A

ans =

5 1 -3
-2 17 12
-5 23 18

 

[Chony]

Thanks, You rock!

 

[Lathentar]

I know.