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A determinant (which uses vertical lines instead of brackets)

| row 1: 1 , -3  row 2: 5 , 7 |

will give us a number that goes along with the matrix.  We'll be able to use these numbers to solve systems!  Woo hoo!

OK, so here's how you get the determinant -- it's really easy:

| row 1: 1 , -3  row 2: 5 , 7 | = ( 1 ) ( 7 ) - ( 5 ) ( -3 ) = 22

Here's what I did:

I multiplied down this diagonal...

| top row: 1 , -3  bottom row: 5 , 7 | ... multiply down diagonally through the 1 and the 7 = ( 1 ) ( 7 )

| top row: 1 , -3  bottom row: 5 , 7 | = ( 1 ) ( 7 ) - Put a minus...

then multiplied up this diagonal...

| top row: 1 , -3  bottom row: 5 , 7 | ... multiply up diagonally through 5 and -3 = ( 1 ) ( 7 ) - ( 5 ) ( -3 ) = 22

 

Here's the general formula:

| top row: a , b  bottom row: c , d | = ad - cb

 


TRY IT:

| top row: -2 , -6  bottom row: 5 , 8 | =

| top row: 3 , 9  bottom row: 2 , 6 |