How much money did Bart save in interest by using a 3 year loan rather than a 5 year loan

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

How many solutions does the equation have? 4x+19=-9-6x

valentinak56 [21]

Answer:

one solution; x= -28/10

Step-by-step explanation:

5 0

3 years ago

What is the answer for: 7 - 8(x-3)=x-14

ikadub [295]

Answer:

1. x=5

2.x=-33/8

3.x=10

4.x=5

Step-by-step explanation:

5 0

3 years ago

Increase 840 in the ratio 2 : 3

Iteru [2.4K]

Ratios be 2x and 3x

$\\ \rm\longmapsto 2x+3x=840$

$\\ \rm\longmapsto 5x=840$

$\\ \rm\longmapsto x=\dfrac{840}{5}$

$\\ \rm\longmapsto x=168$

Now

2x=2(168)=336
3x=3(168)=508

3 0

3 years ago

Read 2 more answers

4. Two friends, Sequoia and Raven, sold organic chap sticks at the local market.

Nina [5.8K]

Answer:

Sequoia sold 2 chap sticks while Raven sold 4.

Step-by-step explanation:

Since two friends, Sequoia and Raven, sold organic chap sticks at the local market, and Sequoia sold her chap sticks for $ 4 and Raven sold hers for $ 3 each, and in the first hour, their total combined sales were $ 20, if in the first hour, the friends sold a total of 6 chap sticks between them, to determine the number of chap sticks each of the friends sold during this time the following calculation must be performed:

6 x 4 + 0 x 3 = 24

5 x 4 + 1 x 3 = 23

2 x 4 + 4 x 3 = 20

Therefore, Sequoia sold 2 chap sticks while Raven sold 4.

7 0

3 years ago