A. (0,5) B. (0,2) C. (-1,3) D. (-3,-1)

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

3 years ago

Is a square a type of rectangle or is a rectangle a type of square? Explain why or why not?

GaryK [48]

Answer:

A square is a rectangle.

Step-by-step explanation:

A square is a quadrilateral with all four angles right angles and all four sides of the same length. So a square is a special kind of rectangle, it is one where all the sides have the same length. Which means, every square is a rectangle because it is a quadrilateral with all four angles right angles.

4 0

3 years ago

Read 2 more answers

Calculate the sum of the multiples of 4 from 0 to 1000

allochka39001 [22]

Answer:

sum is 125,500

sum in summation notation is $\sum\limits_{n=0}^n a+nd$ = (2a+(n-1)d)n/2

Step-by-step explanation:

This problem can be solved using concept of arithmetic progression.

The sum of n term terms in arithmetic progression is given by

sum = (2a+(n-1)d)n/2

where

a is the first term

d is the common difference of arithmetic progression

_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

d = 8-4 = 4

d can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

we have last term as 1000

Nth term can be described

Nth term = 0+(n-1)d

1000 = (n-1)4

=> 1000 = 4n -4

=> 1000 + 4= 4n

=> n = 1004/4 = 251

_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

= (2*0 + (251-1)4)251/2

= (250*4)251/2

= 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

sum in summation notation is $\sum\limits_{n=0}^n a+nd$ = (2a+(n-1)d)n/2

3 0

3 years ago

12+[ 9 4/5 - ( 1.5 + 2 2/10)] Someone please help me?

lord [1]

Answer:

18.1

The thing You NEEDED to do

<h3>Simplify or Evaluate Your Answer</h3>

5 0

3 years ago

Your parents purchase a computer for $1,257.00 plus 6% sales tax. They decide to finance it through the store’s 0% program for 6

Katena32 [7]

Answer:

$111.59

Step-by-step explanation:

The total amount of the purchase was the cost of the computer plus the sales tax:

$1,257*1,06= $1,332.42

Now, to determine the interest that they will have to pay, you have to consider that the interest rate is 16,75% APR that is the annual percentage rate but as only 6 month have passed, the interest rate at this point that they have to pay is 8.375%:

$1,332.42*8.375%= $111.59

The interest that they will be charged is $111.59

5 0

3 years ago