Question

Hi Guys, we had this question where we they gave us two matrices which I will show below, first one has a determinant of 4 and we needed to select and answer for the determinant of the second matrix, my answer was 4, the lecturer's answer was 24.
If the matrix | a b c || d e f | = 4| g h i |
What is the below matrix equal to?| (g+2a) (h+2b) (i + 2c) |
| 3a 3b 3c | | 2d 2e 2f |

appologies it does not seem that this question displays correctly...

Answer 1

sorry don't know matrices

Answer 2

doesn't it have to be a square matrix to find determinant ?

Answer 3

It is square just did not display correctly above: Matrix 1) Row1: |a b c| Row2: |d e f| Row3: |g h i| Matrix 2) Row1: |(g + 2a) (h + 2b) (i+2c)| Row2: |3a 3b c3| Row 3: |2d 2e 2f|

Answer 4

oh got it, thanks

Answer 5

so this deals with how row operations on a matrix affects the determinant

http://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant

anyways moving the rows has no affect
adding rows has no affect
multiplying a row by constant changes determinant by same factor

Answer 6

2*3 = 6
so the determinant is changed by factor of 6
4*6 = 24

Answer 7

Thanks! I will go back and have a look at this, so even though a matrix is multiples of another, the determinant will not be equal?

Answer 8

no because in the process of getting derterminant you are multiplying those coefficients which increases the determinant of new matrix proportionately