Expert: Sherry Wallin - 9/24/2011

Question
QUESTION: question is in the image

ANSWER:     | 1 5 8 |
x | 0 2 6 |
  | 0 0 3 |

Since there are three zeros in the first column of 4 all you need to do is calculate the determinant of the matrix above because the other 3x3 matrices will be being multiplied by 0 and result in 0. In this one matrix you have two zeros in the first column of three numbers so the only non zero term is x(2*3-0*6) = 6x and since 6x is also the number of combinations of 4 things taken at least 1 at a time  you want 6x to equal
4C1 + 4C2 + 4C3 + 4C4 = 4 + 6 + 4 +1 = 15 => 6x = 15 so x = 5/2

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Sir I am a class eleventh student and could not understand your solution .Plzzz explain clearly

Answer
If you have a 2x2 matrix and you want to find the determinant you multiply the element in the 1st row and 1st col by the element in the 2nd row 2nd col and the subtract off the product of the 2nd row 1st col times the 1st row 2nd col. This is standard for a 2x2 determinaht

| a  b |   = ad-bc
| c  d |
When you have a 3x3 determinant you will do like this:

| a  b  c |
| d  e  f | = pivot on any row or col, I choose col 1: a* det (e, f, i, j) - b*det (d, j, h, f) + c* det(d, i, h, e)    
| h  i  j |          
         

and with the 4x4 determinant you break it down into 2x2 determinants. Any time you have a row or  col of zeros you will have 0* det of something and it will be zero as well so in your 4x4 determinant we lose all the sub determinants because you have a column of zeros.

Math Prof