Exercise 20
2x+5y-10z-100=0
4x-10y+20z-150=0
8x+8y+15z=300
 2x+5y-10z=100
4x-10y+20z=150
8x+8y+15z=300
ANSWER
DET A
2
4
8
5
-10
8
-10
20
15
2
4
8
5
-10
8
Det A= [(2.-10.15)+(5.20.8)+(-10.4.8)-(8.-10.-10)+(8.20.2)+(15.4.5)]
= -300+ 800+ (-320)-800 + 320+ 300
= 180-1420
= -1240
DET X
100
150
300
5
-10
8
-10
20
15
100
150
300
5
-10
8
Det X = [(100.-10.15)+(5.20.300)+(-10.150.8)-(300.10.10)+(8.20.100)+(15.150.5)]
= -15000+30000+(-12000)-30000+16000+11250
=3000-57250
=-54250
DET Y
2
4
8
100
150
300
-10
20
15
2
4
8
100
150
300
Det Y = [(2.150.15)+(100.20.8)+(-10.4.300)-(8.150.10)+(300.20.2)+(15.4.100)]
= 4500+16000+(-12000)-(-12000)+12000+6000
= 8500-6000
= 2500
DET Z
2
4
8
5
-10
8
100
150
300
2
4
8
5
-10
8
Det Z =[(2.-10.300)+(5.150.8)+(100.4.8)-(8.-10.100)+(8.150.2)+(300.4.5)]
= -6000+6000+3200-(-8000)+2400+6000
= 3200-400
= 2800
o DET X  -54250/-1240 = 43,75
o DET Y  2500/-1240 = -2,01
o DET Z  2800/-1240 = -2,25
EXERCISE 21
2x+5y-10z-100=0
4x-10y+20z-150=0
8x+8y+15z=300
 2x+5y-0z=100
4x-10y+0z=150
8x+8y+0z=300
ANSWER
DET A
2
4
8
5
-10
8
0
0
0
2
4
8
5
-10
8
Det A = [(2.-10.0)+(5.0.8)+(-0.4.8)-(8.-10.0)+(8.0.2)+(0.4.5)]
=0
DET X
100
150
300
5
-10
8
0
0
0
100
150
300
5
-10
8
Det X =[(100.-10.0)+(5.0.300)+(-0.150.8)-(300.-10.0)+(8.0.100)+(0.150.5)]
=0
DET Y
2
4
8
100
150
300
0
0
0
2
4
8
100
150
300
Det Y =[(2.150.0)+(100.0.8)+(-0.4.300)-(8.150.0)+(300.0.2)+(0.4.100)]
=0
DET Z
2
4
8
5
-10
8
100
150
300
2
4
8
5
-10
8
Det Z =[(2.-10.300)+(5.150.8)+(100.4.8)-(8.-10.100)+(8.150.2)+(300.4.5)]
= -6000+6000+3200-(-8000)+2400+6000
= 3200-400
=2800
o DET X 0/0 = o DET Y 0/0 = o DET Z  2800/0 = -