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...
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sorry don't know matrices
doesn't it have to be a square matrix to find determinant ?
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|
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oh got it, thanks
so this deals with how row operations on a matrix affects the determinant
anyways moving the rows has no affect
adding rows has no affect
multiplying a row by constant changes determinant by same factor
2*3 = 6
so the determinant is changed by factor of 6
4*6 = 24
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?
no because in the process of getting derterminant you are multiplying those coefficients which increases the determinant of new matrix proportionately