Fill in the blank with the correct response.

Can you tell me how to calculate R for below Matrix ?

scoray [572]

Answer:

The rank of the matrix is 3.

Step-by-step explanation:

Consider the prided information.

$x=\begin{bmatrix}x_1\\ x_2\\ x_3\end{bmatrix}=\begin{bmatrix}9&2&6&5&8\\ 12&8&6&4&10\\ 3&4&0&2&1\end{bmatrix}$

Reduce the matrix in row echelon form as shown:

$R_1\:\leftrightarrow \:R_2\begin{bmatrix}12&8&6&4&10\\ 9&2&6&5&8\\ 3&4&0&2&1\end{bmatrix}\\$

$R_2\:\leftarrow \:R_2-\frac{3}{4}\cdot \:R_1\ and\ R_3\:\leftarrow \:R_3-\frac{1}{4}\cdot \:R_1\\\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&2&-\frac{3}{2}&1&-\frac{3}{2}\end{bmatrix}$

$R_3\:\leftarrow \:R_3+\frac{1}{2}\cdot \:R_2\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&0&-\frac{3}{4}&2&-\frac{5}{4}\end{bmatrix}$

$R_2\:\leftarrow \:R_2-\frac{3}{2}\cdot \:R_3\ and\ R_1\:\leftarrow \:R_1-6\cdot \:R_3\\\begin{bmatrix}12&8&0&20&0\\ 0&-4&0&6&-2\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}\\R_2\:\leftarrow \:-\frac{1}{4}\cdot \:R_2\ , \ R_1\:\leftarrow \:R_1-8\cdot \:R_2\ and\ \:R_1\:\leftarrow \frac{1}{12}\cdot \:R_1\\\begin{bmatrix}1&0&0&\frac{8}{3}&-\frac{1}{3}\\ 0&1&0&-\frac{3}{2}&\frac{1}{2}\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}$

The rank of a matrix is the number of non zeros rows.

Thus, the rank of the matrix is 3.

6 0

3 years ago

One book costs one pound ninety five pence How much do six books cost

Jobisdone [24]

To determine the total cost of the books, multiply the amount per book with the number of books. In this example, each book costs one pound and ninety-five pence. Converting 95 pence to pound gives 0.95 pounds. Therefore, the cost of each book is 1.95 pounds. Multiply this amount by six, we get 11.7 pounds. Thus, six books cost 11 pounds and 70 pence.

4 0

3 years ago

Submarine a is position at -1100 feet in relation to sea level. Submarine be is position at -800 feet in relation to sea level.

Natasha_Volkova [10]

Answer:

<u>Submarine A needs to travel at 30 feet per minute and the Submarine B at a lower speed, 20 feet per minute. </u>

Step-by-step explanation:

This is the information given to solve the question:

Submarine A position = - 1,100 feet

Submarine B position = - 800 feet

New position for Submarine A and B = - 200 feet

Duration of the travel = 30 minutes

Distance that Submarine A need to travel = - 200 + 1,100 = 900 feet

Distance that Submarine B need to travel = - 200 + 800 = 600 feet

For calculating the speed, we do this new calculation:

Speed Submarine A = Distance that Submarine A need to travel/Duration of the travel

Speed Submarine A = 900 feet/30 minutes

Speed Submarine A = 30 feet/minute (Dividing by 30)

Speed Submarine B = 600 feet/30 minutes

Speed Submarine B = 20 feet/minute (Dividing by 30)

<u>Submarine A needs to travel at 30 feet per minute and the Submarine B at a lower speed, 20 feet per minute. </u>

7 0

3 years ago

Read 2 more answers

Is the first question correct pls correct me if I’m wrong pls pls help on the chart and the last question which is how many hour

baherus [9]

Answer:

First one is correct. The second is 20 hours

Step-by-step explanation:

20 hours

6 0

3 years ago

Which of the following is the final step in bisecting a line segment?

yulyashka [42]

Answer:

B) Mark the intersection points of the arcs, and draw a line through those two points.

5 0

3 years ago