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
Strike441 [17]
3 years ago
11

Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTI

ON.)x1 − 3x2 − 2x3 = 0−x1 + 2x2 + x3 = 02x1 + 3x2 + 5x3 = 0
Mathematics
1 answer:
cricket20 [7]3 years ago
7 0

Answer:

The system has infinitely many solutions

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

Step-by-step explanation:

Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

There are three elementary matrix row operations:

  1. Switch any two rows
  2. Multiply a row by a nonzero constant
  3. Add one row to another

To solve the following system

\begin{array}{ccccc}x_1&-3x_2&-2x_3&=&0\\-x_1&2x_2&x_3&=&0\\2x_1&+3x_2&+5x_3&=&0\end{array}

Step 1: Transform the augmented matrix to the reduced row echelon form

\left[ \begin{array}{cccc} 1 & -3 & -2 & 0 \\\\ -1 & 2 & 1 & 0 \\\\ 2 & 3 & 5 & 0 \end{array} \right]

This matrix can be transformed by a sequence of elementary row operations

Row Operation 1: add 1 times the 1st row to the 2nd row

Row Operation 2: add -2 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1

Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

to the matrix

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

The reduced row echelon form of the augmented matrix is

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

which corresponds to the system

\begin{array}{ccccc}x_1&&-x_3&=&0\\&x_2&+x_3&=&0\\&&0&=&0\end{array}

The system has infinitely many solutions.

\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}

You might be interested in
5 apples cost $7.50. Find the cost of 6 apples. please explain
butalik [34]

Answer:

$9

Step-by-step explanation:

7.50/5= $1.5 an apple

6* 1.5 = $9 for 6 apples

4 0
3 years ago
Read 2 more answers
20×+4=4(5x+1) how many solution are in this equation
Tomtit [17]

Simplify both sides of the equation

(20)(4)= 4(5x+1)

Simplify

80 = 20x+4

Flip the equation

20x+4 = 80

Subtract 4 from both sides

20x+4-4 = 80-4

20x = 76

Divide both sides by 20

20x/20 = 76/20

x= 3.8


There is one solution in this equation

7 0
3 years ago
What type of relationship is indicated by the following set of ordered pairs ? I don’t understand it .
shtirl [24]

Answer: Since the second differences are constant, there is a quadratic relationship between and .

Step-by-step explanation:

7 0
3 years ago
The newspaper headline states there are about 400,000 people in attendance if the newspaper rounded to the nearest 10,000 what i
Radda [10]
Lowest 395,000 / highest 404,999
3 0
3 years ago
Which number sentence could you use to find out how meny bags of chips she bought?
katrin2010 [14]
Are a and c the same?
7 0
3 years ago
Read 2 more answers
Other questions:
  • Solve for x. i will leave pictuere below
    15·2 answers
  • If a cube has a surface area of 150 in squared, what is the length of one of the sides
    10·1 answer
  • How many edges must be removed from the wheel graph W6 in order to create a spanning tree for the graph?
    8·1 answer
  • What is the value of x?<br><br> x = ___
    13·1 answer
  • There are 16 pool balls on the table. If you shoot all of the solid balls in on the first turn how many different ways can they
    14·1 answer
  • Find the value of x. 1) m angle2=3x-6 120° 2 B) 10 D) 6 A) 12 C) -11​
    6·1 answer
  • Will GiVE BRAINLIEST!!!!
    10·1 answer
  • SEPTEMBER 2016 (GP HYPERBOLA)
    10·1 answer
  • Can someone help me please
    8·1 answer
  • What is the median of the data set?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!