Solve by multiplying and adding.Top- {g=3h-20 and bottom h-g=.4?

Question

Its like matrix kind of stuff.

Answer 1

This looks like a system of simultaneous equations.

h-g=0.4 so g=h-0.4 and g=3h-20 becomes h-0.4=3h-20, 19.6=2h, so h=9.8.

g=h-0.4=9.8-0.4=9.4. Solution is (g,h)=(9.4,9.8).

To solve using matrices:

Rewrite the equations: g-3h=-20, -g+h=0.4.

In matrix form the equations become:

(  1   -3 )( g ) = ( -20 )

( -1   1 )( h )     ( 0.4 )

First work out the determinant D:

|  1   -3 |

| -1    1 | = (1)(1)-(-3)(-1) = 1-3 = -2, so D=-2.

Find g:

| -20 -3 |

| 0.4  1 | = (-20)(1)-(-3)(0.4) = -20+1.2 = -18.8, g=-18.8/D = 9.4

Find h:

|  1 -20 |

| -1 0.4 | = (1)(0.4)-(-20)(-1) = 0.4-20 = -19.6, h=-19.6/D = 9.8