Expert: Steve Holleran - 7/19/2008

Question
I saw this on a test and I have no idea what it is. The question asked me to solve the following:
|  3 3 |
| -2 2 |

(The vertical lines were not broken)

Answer
Hi Josh,

Well, I'll take my best guess here and tell you it looks like a determinant.  

I don't know if you are aware of what a "matrix" is, but its just any rectangular array of numbers, usually grouped in a BIG parenthesis or set of brackets ([).  Like :

A = [ 1  3  -2

      -4 0   6]     is called a 2 by 3 matrix (it's always
                    rows by columns).

Any matrix with an equal number of rows and columns is called a square matrix.  Using your numbers above, this is a 2 by 2 square matrix:

                     [ 3  3

                      -2  2]

If a matrix is square, then it has what's called a determinant, and this  is what I think you have here.  A determinant of a square matrix is always shown by using vertical bars instead of brackets or parentheses, kind of like large absolute value bars.

I guess by "solve", you mean compute the value, so for a 2 by 2 matrix  that looks like :

                    A = [a  b

                         c  d]

the determinant is shown by

              det(A) = |a  b|
                       |c  d| = a*d - b*c  (the ad diagonal minus
                                            the bc diagonal)

So, for this determinant, we would have:

               | 3  3|
               |-2  2|  = (3 * 2) - (-2 * 3)= 6 - (-6) = 12.

Good thing you didn't have a 3 by 3 matrix, the determinant is much, much harder to compute!!

Hope this helps,
Steve