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A matrix is just a grid of numbers inside brackets. When it's a coefficient matrix the coefficients are the entries. The coefficient matrix here is:

Example 2

What are the rows and columns in the matrix:

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

Row one = 3x -5y, row two = -2xy: column one = 3x -2x, column two = -5yy.

Example 3

Find D, the determinant of the coefficient matrix from Example One above:

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)

Example 4

Find D from this matrix:

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

We know thanks to the formula that to find D 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):