Hi,
I didn't get so well what this problem is asking. Mostly how the B matrix is generated.
Let . The matrix B is generated by the matrix A by addition of the multiple of the j-th row to the i-th row ( ). Show that detB = detA.
Hi,
I didn't get so well what this problem is asking. Mostly how the B matrix is generated.
Let . The matrix B is generated by the matrix A by addition of the multiple of the j-th row to the i-th row ( ). Show that detB = detA.
For example, if and B "is generated by the matrix A by addition of the multiple of the 3rd row the the first row" (taking j= 3 and i= 1), then .
A determinant is a sum of products, each of which involves exactly one factor from each row. Here, such a product, will be replace by . Multiply that out.