Use the Gauss Jonlan mthod to solve each system of equations. 4x-3y+z+w=21, -2x-y+2z+7w=2, 10x-5z-20w=15?

Question

Use the Gauss Jonlan mthod to solve each system of equations.
4x-3y+z+w=21
-2x-y+2z+7w=2
10x-5z-20w=15

Answer 1

Hi,
First I’ll define some “shorthand” that I’ll be using: -2R1 +R2 -->R2 means multiply row 1 by -2, add that to row 2 and replace row 2 with the result. From this you should be able to interpret the other operations
This is not a good system to solve as you’ll soon see. First let’s swap rows 1 and 2, we’ll have this matrix:
[-2…-1…2…7……2]
[4….-3…1….1…..21]
[10…0…-5…-20..15]

[-2…-1…2…7……2]
[0….-5…5….15…..25]…2R1 +R2-->R2
[0…-5…5…...15.....25]…5R1+R3-->R3
Since rows 2 and 3 are now identical, we can set row 3 equal to zero since if we added
-R1+R20. So, we now have this matrix:

[-2…-1…2…7……2]
[0….-5…5….15…..25]
[0… 0…0…..0......0]…

[-2….0…1…4……-3]….R2+R1-->R1
[0……1.-1….-3…..-5]…(-1/5)R2
[0… 0…0…..0......0]

[1….0…-0.5…-2…-1.5]….(-1/2)R1
[0…1…..-1….-3…..-5]…(-1/5)R2
[0…0……0…..0......0]…

As you can see, this is not much of a solution. You could write the variables in terms of other variables if your text requires that, but in essence, you must assign values to some of the variables to get a value for any one variable.

Incidentally, you can solve this easily with a graphing calculator. If you don't know how to do that and are interested, see my Website:
www.angelfire.com/pro/fkizer
and look in the TI-83 Plus User Guide.

FE

Answer 2

3y + 2Z = 12 y - z = 9. from the 2d: y = z+9 substitute into the 1st 3(z+9) + 2z = 12 3z + 27 + 2z = 12 5z + 27 = 12 subtract 27 from the two facets 5z = -15 divide via 5 z = -3 y = z+9 = -3+9 = 6 the respond is C.