Please help im stuck

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

cricket20 [7]

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:

Switch any two rows
Multiply a row by a nonzero constant
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.

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

7 0

2 years ago

How do i solve this quadratic equation x²+6x+c

Anuta_ua [19.1K]

recall in a perfect square trinomial, the middle term is the tale-tell guy, we know the middle term is the product of 2 and the two other guys without the exponent, so in this case 6x = 2*√x² * √c.

$\bf 6x=2\cdot \sqrt{x^2}\cdot \sqrt{c}\implies 6x=2\sqrt{x^2c}\implies 6x=2x\sqrt{c}\\\\\\\cfrac{6x}{2x}=\sqrt{c}\implies 3=\sqrt{c}\implies 3^2=c\implies 9=c$

6 0

3 years ago

Answer & explanation please..30 points?

inn [45]

Looks like 75%. Not sure what they're talking about for the reduce part.

7 0

2 years ago

- 3(3s - 4) - 12 = - 3/6s + 1) - 4

s344n2d4d5 [400]

Answer:

s=-7/9

Step-by-step explanation:

-9s+12-12=-18s-3-4

-9s=-18s-7

9s=-7

s=-7/9

(if I understood the question correctly)

6 0

2 years ago

If $396 is invested at an interest rate of 13% per year and is compound continuously, how much will the investment be worth in 3

Sveta_85 [38]

Answer:

The investment at the end of the period will be $584.89.

Step-by-step explanation:

FV = PV e⁽ⁿˣ⁾

FV = Future Value = ?

PV = Present Value = $396

n = Interest Rate = 13%

x = time in years = 3

e = mathematical constant = 2.7183

FV = 396 x 2.7183⁽⁰°¹³ ˣ ³⁾

FV = 396 x 1.4770

FV = $584.89

7 0

3 years ago