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.

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- May 10th 2010, 02:41 AMTheFangelDeterminant of two matrices
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. - May 10th 2010, 03:34 AMHallsofIvy
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. - May 11th 2010, 05:06 AMTheFangel
Wow!

Thanks very much!