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Expert: Sherry Wallin - 2/12/2011


Question
Find the value of
'            '
'-1   0   -1 '
'            '
' 0  -1   -1 '             
'            '
'-1  -1    0 '
'            '

Answer

determinant
Dhananjay~

To find the determinant of a 3x3 matrix you need to choose whether you want to operate on a row or column and then draw a line through the first row and the first column and calculate the determinant of the 2x2 matrix that is left using the element in the first row first column as the multiplier. In your case I chose to use the first column as my operator so that is -1(-1*0--1*-1) = -1(1*-1) = 1
Now go to the 2nd element in column 1 (it will be your next multiplier) and cross out the first column and 2nd row and find the determinant of the remaining 2x2 matrix: 0*(0*0--1*-1) **Note when the multiplier is 0 the whole product will be 0 so it really isn't necessary to do anything but realize you have 0 in your sum that you are acquiring. Now go to the 3rd element in the 1st column and -1 is your multiplier and cross out the first column and 3rd row and find the determinant of the remaining 2x2 matrix as before: -1*(0*-1--1*-1) = -1(0+1*-1) = -1(-1) = 1
So the determinant of this 3x3 matrix is the sum of the three 2x2 matrices determinants that you calculated: 1 + 0 + 1 = 2

One crucial thing you need to note is that the 'sign' on the multiplier may change depending on which element it is. The 'rule' is that you alternate +-+-... in the row or column that you use for your multiplier. In our case the first multiplier is + -1, which is what we used and the 2nd multiplier was 0 so it doesn't matter what sign you use, and the 3rd multiplier will again we + so it is +-1, which is what we used.

I will attached an image of what I am talking about to help you see what I did.

Math Prof
    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentThanks a lot for your valuable input


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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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