SOLUTION: Hi all, I had a similiar question to this earlier, and was hoping to get help with this one also. For the given Matrix A = (1 2 3) 2 1 -1 2 0 1 a) Find det A by expan

Algebra ->  Functions -> SOLUTION: Hi all, I had a similiar question to this earlier, and was hoping to get help with this one also. For the given Matrix A = (1 2 3) 2 1 -1 2 0 1 a) Find det A by expan      Log On


   

Question 204663: Hi all, I had a similiar question to this earlier, and was hoping to get help with this one also.
For the given Matrix
A =
(1 2 3)
2 1 -1
2 0 1
a) Find det A by expanding row 1
b) Confirm answer by expanding by column 2. Then explain breifly how you know that answer is the same.
Any help with the above would be most appreciated.
Thanks, -Nick.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
For the given Matrix
A = abs%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C1%2C-1%2C2%2C0%2C1%29%29
a) Find det A by expanding row 1

Expanding about row 1:

abs%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C1%2C-1%2C2%2C0%2C1%29%29

b) Confirm answer by expanding by column 2.

Expanding about column 2:

abs%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C1%2Cf%2C2%2C0%2C1%29%29

Then explain breifly how you know that answer is the same.
Any help with the above would be most appreciated.

Take this general 3x3 matrix:

abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

Expanding about row 1:



Expanding about column 2:

abs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29



And you can see that they are equal, for only the order of terms
and their factors are different. 

Edwin