1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanya [424]
3 years ago
8

Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent m

atrix in reduced row echelon form. (Show the steps in the process of converting to G-J). You don't have to find the solution set X12x223 = 6 2a1 3 = 6 X1x23x3 = 6
Mathematics
1 answer:
Rasek [7]3 years ago
4 0

Answer:

System of equations:

x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6

Augmented matrix:

\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]

Reduced Row Echelon matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]

Step-by-step explanation:

Convert the system into an augmented matrix:

\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

R_2=-2r_1+r_2\\R_3=-r_1+r_3

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right]

2. Operations:

R_2=-\frac{1}{3}r_2

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right]

3. Operations:

R_3=r_2+r_3

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right]

4. Operations:

R_3=\frac{1}{2}r_3

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]

You might be interested in
Martin is 6 years younger than his sister. The sum of their ages is no more than 22 years.
Kobotan [32]

So their age can be no more than 22. And Martin is 6 years younger, which means you subtract.

22 ≥ x + x - 6

5 0
3 years ago
Bonjour j’ai un exercice de maths et je ne comprends rien
Minchanka [31]
Donc pour trouver la réduction de 30% nous allons trouver 30% de 49 alors nous allons faire 30 × 100 × 49 = 14,7 14,7 est la réduction maintenant nous devons faire 49 € -14,7 € soit 34,3 €, le prix est maintenant de 34,3 €, désolé d'utiliser Google Translate pour vous aider, mais j'espère que c'est correct :)
4 0
3 years ago
Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). Write the equati
Nutka1998 [239]

the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.

it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.

check the picture below.

so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)


\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9


\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill

7 0
3 years ago
PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!
Semenov [28]

Answer:

1/20

Alternate from 0.05, 20 - 1

Hope this helps

7 0
3 years ago
Read 2 more answers
If f(x)=6-2x, Find the value for f(-1)
Katarina [22]

Answer:

f(-1)=8

Step-by-step explanation:

Just plug in x=-1 into the function:

f(x)=6-2x

y=6-2(-1)

y=6+2

y=8

So f(-1)=8

7 0
3 years ago
Other questions:
  • What is the answer to this following equation (2•5)-56+102(4•215)
    9·1 answer
  • Roger bought some turkey and some roast beef for the soccer club picnic. He said $150 for a total of 20 pounds of meat. the turk
    15·1 answer
  • Pls help me with this!!!
    14·1 answer
  • 111 = 14a This part is for the extra characters
    9·1 answer
  • Which of the following can be written as the sum of 2 prime numbers
    12·2 answers
  • A washing machine can hold
    15·1 answer
  • Shirts by Sam Might-T Shirts
    5·1 answer
  • Pls help thanks i need this ty ty
    13·1 answer
  • Convert 12/5 into a decimal
    10·2 answers
  • 1.1.3 Quiz: What Is a Function?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!