Algebra Know-It-ALL

Here are the equations, derived directly from the coefficients in the matrix:

0 x+ 4 y+ (−z)=− 2

5 x+ (−3/2)y+ 8 z= 1

x+y+z= 1

Here are the equations with the negative additions converted to subtractions, and the

term 0x eliminated from the first equation for simplicity:

4 y−z=− 2

5 x− (3/2)y+ 8 z= 1

x+y+z= 1

4. Here’s the matrix again, for reference:

04 − 1 − 2

(^5) −3/2 81
1111
Let’s interchange the first and second rows. Then we get
5 −3/2 81
04 − 1 − 2
11 1 1
If we multiply the first row by 2 to get rid of the fractional expression, we have
(^10) − 3 16 2
04 − 1 − 2
1111
We can multiply the bottom row by −10, getting
10 − 3 16 2
(^04) − 1 − 2
− 10 − 10 − 10 − 10
Adding the first row to the third and then replacing the third row with the sum, we obtain
(^10) − 3 16 2
(^04) − 1 − 2
0 − 13 6 − 8
Chapter 19 657