00:01
In this problem we have given a determinant here given this determinant a 1 a 2 a 3 b1 b2 b 3 c 1 c 2 c 3 so this determinant equal to minus 5 then we have to find then we have to find here c 1 c 2 c3 and minus b1 minus b2 minus b3 and a 1 a 2 a 2 a 3 we have to find this value how to find this we will use here properties of properties of determinant that is if we have any matrix let's say determinant of the matrix a b c d e f g h i if we want to convert any row or we want to interchange with any row to other rows if we want to convert r1 to r3 so by by interchange with any rows any two rows we have minus of this sign so if if we want to convert r1 to r3 so r3 will come here g h i and d e f and r1 will come here in place of r3 a b c overall after one interchange we have one minus sign now also if we have any matrix and determinant of this matrix and if we multiply by a constant in a single row then let's let's see you multiply by a constant in a single row then let's assume here a b c and let's write multiply by k into second row so k d k e and k f and g h i if we multiply k in a single row so this is the k into a b c d g f g h i these two property we will use here since we have given this a1, a2, a3, b1, b2, b3 and c1, c2, c3 equal minus 5.
03:02
Now using this first property, if we interchange the row 1 by row 3 or the third row we will have here by interchanging r1 to r3, row 1 to row 3.
03:19
That is c1 c1 will come here c1 c2 c3 b1 b2 b3 and a1 a2 a3 so after interchanging first row with third row we will have one minus sign here minus of minus 5 or we can write it as minus of a 1 a 2 a 3 b1, b2, b3, c1, c2, c3, that is minus of minus 5 equal 5.
04:07
So we have this is equal 5, b3, and a1, a2, a3 equal.
04:23
Now if we multiply here minus 1 into the second row, so using the second property that we have written here, if we want to multiply by a constant in a single row, then that constant is multiplied by whole determinant...