Question

2. Given the System of Equations:

3x+2y+z+20w= 6

x+2y+z+10w=0

x+y+z+6w=2

2x+2y+z+15w=3

a) Use your calculator to solve, leaving solution in parametric form

b) Find the specific solution when y = 6

c) Perform, BY HAND, a full check of this particular solution

Answer 1

system is

augmented matrix is

3	2	1	20	6
1	2	1	10	0
1	1	1	6	2
2	2	1	15	3

convert into Reduced Row Eschelon Form...

Divide row1 by 3

1	2/3	1/3	20/3	2
1	2	1	10	0
1	1	1	6	2
2	2	1	15	3

Add (-1 * row1) to row2

1	2/3	1/3	20/3	2
0	4/3	2/3	10/3	-2
1	1	1	6	2
2	2	1	15	3

Add (-1 * row1) to row3

1	2/3	1/3	20/3	2
0	4/3	2/3	10/3	-2
0	1/3	2/3	-2/3	0
2	2	1	15	3

Add (-2 * row1) to row4

1	2/3	1/3	20/3	2
0	4/3	2/3	10/3	-2
0	1/3	2/3	-2/3	0
0	2/3	1/3	5/3	-1

Divide row2 by 4/3

1	2/3	1/3	20/3	2
0	1	1/2	5/2	-3/2
0	1/3	2/3	-2/3	0
0	2/3	1/3	5/3	-1

Add (-1/3 * row2) to row3

1	2/3	1/3	20/3	2
0	1	1/2	5/2	-3/2
0	0	1/2	-3/2	1/2
0	2/3	1/3	5/3	-1

Add (-2/3 * row2) to row4

1	2/3	1/3	20/3	2
0	1	1/2	5/2	-3/2
0	0	1/2	-3/2	1/2
0	0	0	0	0

Divide row3 by 1/2

1	2/3	1/3	20/3	2
0	1	1/2	5/2	-3/2
0	0	1	-3	1
0	0	0	0	0

Add (-1/2 * row3) to row2

1	2/3	1/3	20/3	2
0	1	0	4	-2
0	0	1	-3	1
0	0	0	0	0

Add (-1/3 * row3) to row1

1	2/3	0	23/3	5/3
0	1	0	4	-2
0	0	1	-3	1
0	0	0	0	0

Add (-2/3 * row2) to row1

1	0	0	5	3
0	1	0	4	-2
0	0	1	-3	1
0	0	0	0	0

reduced matrix is

.........................free variable

.

general solution is

here

when y=6

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when y=6, solution is