How do you solve ((8, 7), (1, 1))x=((3, -6), (-2, 9))?

1 Answer
Aug 14, 2018

x = ((17,-69),(-19,78))

Explanation:

Let's try multiplying both sides by ((1, -7), (-1, 8)) and see what happens:

((1, -7),(-1, 8))((8, 7),(1,1))x=((1,0),(0,1))x = x

whereas:

((1, -7),(-1,8))((3,-6),(-2,9)) = ((17,-69),(-19,78))

So:

x = ((1, -7),(-1, 8))((8, 7),(1,1))x = ((1, -7),(-1,8))((3,-6),(-2,9)) = ((17,-69),(-19,78))

In general, the multiplicative inverse of ((a,b),(c,d)) is:

1/abs((a,b),(c,d)) ((d, -b),(-c, a))

and in our example:

abs((8, 7),(1, 1)) = 8 * 1 - 7 * 1 = 8 - 7 = 1