What are the rows and columns in the following matrix?

The rows of a matrix are the horizontal number groups, and the columns are the vertical number groups, so in this coefficient matrix the rows and columns are:

Row one = 3x, -5y

Row two = -2x, y

Column one = 3x, -2x

Column two = -5y, y

Find D, the determinant of the following matrix:

To find D, you multiply down the first diagonal:

And up the second:

And put a minus between them. Crisscross minus applesauce.

For this example:

D = (3x)(y) – (-2x)(-5y) = 3xy – 10xy = -7xy

What's the determinant of this matrix?

To find D, the determinant, we put the matrix in bars rather than brackets:

Thanks to the formula, we know thanks that you multiply down the first diagonal and up the second, and then put a minus between them. That's our crisscross applesauce thing (no jump rope needed):

D = (2)(1) – (3)(2) = 2 – 6 = -4