Question

Solve using Gauss Jordan elimination:
WILL GIVE A MEDAL!! :D

Answer 1

\[4x _{1} + 12x _{2} - 24x _{3} = 16\]

Answer 2

\[5x _{1} +15x _{2} - 30x _{3} = 20\]

Answer 3

@Hero , and @genius12 please help me :)

Answer 4

meaning?

Answer 5

2 equations only?

Answer 6

but can u help me find the solution through a step by step

Answer 7

Yes sirm3d only two equations.

Answer 8

@genius12 please assist me with this question

Answer 9

4 12 -24 16
5 15 -30 20

mutliply row 1 by (1/4)
multiply row 2 by (1/5)

1 3 -6 4
1 3 -6 4

multiply row 1 by -1 and add to row 2

1 3 -6 4
0 0 0 0

Answer 10

a row of zeros means that the equation has infinite number of solutions.

Answer 11

@genius12 please assist me with this question

Answer 12

@genius12 please assist me with this question

Answer 13

what is the solution then?

Answer 14

@Hero also assist and @genius12

Answer 15

x_2=s, x_3=t

the first row says \[x_1 + 3x_2 - 6x_3 = 4\]
solving \(x_1\)

\[x_1=4-3x_2+6x_3\] or

\[x_1=4-3s+6t\\x_2=s\\x_3=t\]

Answer 16

There is a infinite number of solutions. Because of this:\[A=\left[\begin{matrix}4 & 12 & -24 & 16 \\ 5 & 15 & -30 & 20\end{matrix}\right]\] If we perform the following row operation on the second row: row2 * 4/5, we get the following matrix:\[A=\left[\begin{matrix}4 & 12 & -24 & 16 \\ 4 & 12 & -24 & 16\end{matrix}\right]\]Since both rows are the exact same, subtracting them would give us 0x1 + 0x2 + 0x3 = 0 or 0 = 0. This indicates an infinite number of solutions.

An easier way to see that this system has infinitely many solutions by first getting values of x1, x2, x3 that satisfy one equation. When these same values are plugged in to the other equation, the equation remains to be true. For example, if I choose 3 values, x1 = 7, x2 = 1, x3 = 1 then plug these in to the first equation, the result is 16. When I plug these values in to the second equation, I get 20.

If: \[x _{1}=7,x _{2}=1,x _{3}=1\]\[4x _{1}+12x _{2}-24x _{3}=16\rightarrow4(7)+12(1)-24(1)=16\rightarrow16=16\]\[5x _{1}+15x _{2}-30 x _{3}=20 \rightarrow5(7)+15(1)-30(1)=20\rightarrow20=20 \]From this we can see that any values that satisfy once equation satisfy the other. Thus system has infintely many solutions.

@Anita505

Answer 17

so the solution is ?

Answer 18

There is no one solution. There is infinitely many solutions, which means that there is an infinite possible sets of x1,x2,x3 which satisfy both equations. It's not a regular system where you get a certain value for each variable. Here you can find infinitely as many to satisfy both equations so there is no single answer for all the variables.

Answer 19

\[x _{1}= ? x _{2}= ? x _{3}= ?\]

Answer 20

x1 = infinite number of possibilities
x2 = infinite number of possibilities
x3 = infinite number of possibilities

You see, this is not a system you are used. Normally you get systems of equations where like you get the answer as, x1 = 2, x3 = 5 or something like that. For questions like that, the system only has that one particular solution.

In this case however, our system of the 2 equations doesn't have an answer like x2 = 3, x1 = 7, x3 = 5, rather there is infinite number of possibilities for each variable which satisfy both equations.

So we write, system has infinitely many solutions.

Answer 21

@Anita505

Answer 22

Oh okay thank you that seems a lot more clear now

Answer 23

so meaning no solution then?

Answer 24

but it says for me to select the correct choice below and fill in the answer boxes within your choice.

b. the system has infinitely many solutions. The solution is x1=____ , x2=___ and x3= t
c. the system has infinitely many solutions. The solution is x1-____, x2= s and x3= t
d. there is no solution.

So what do i write down then?

Answer 25

@genius12

Answer 26

@genius12

Answer 27

thank you Hero :)