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artcher [175]
3 years ago
10

Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form.

Mathematics
1 answer:
Gekata [30.6K]3 years ago
3 0

Take the augmented matrix,

\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right]

Swap the row 1 and row 2:

\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right]

Add -2(row 1) to row 2, and -1(row 1) to row 3:

\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right]

Add -1(row 2) to row 3:

\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right]

Multiply through row 3 by 1/9:

\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right]

Add 5(row 3) to row 2:

\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right]

Multiply through row 2 by -1/3:

\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]

Add -2(row 2) and -1(row 3) to row 1:

\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]

So we have \boxed{x=-3,y=-2,z=4}.

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What is the slope of y-9=3(x-2)<br> A. 3<br> B. 1/2<br> C. 2<br> D. 1/9
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An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3ft long with a diameter of 2.2 ft . S
Contact [7]

4 minutes 34 seconds will takes to empty the tank, if the starts completely full and oil drained at a rate of 2.5 ft^{3} per minute.

Step-by-step explanation:

              The given is,

                         Tank is shaped like a cylinder that is 3 ft long with a diameter of 2.2 ft.

                          Oil drained at a rate of 2.5 ft^{3} per minute.

Step:1

       Time taken to dry the oil tank is,

                           T   = \frac{Volume of oil}{Oil drain rate}  ....................................(1)

Step:2

      Volume of the oil is,

                           V = \pi  r^{2} h.................................................(2)

      Where, r - Radius of Cylinder

                             r = \frac{d}{2}

                             r = \frac{2.2}{2}

                             r = 1.1 ft

      From eqn (1),

                        V =  \pi × 1.1^{2} × 3

                           = 11.40398 ft^{3}

Step:3

     From equation (1)

                           = \frac{11.40398}{2.5}

                           = 4.56

                           = 4.56 minutes

                      T  = 4 minutes 34 seconds

Result:

      Time taken to dry the oil tank is 4 minutes 34 seconds, if a cylinder is 3 ft long with a diameter of 2.2 ft and oil is drained at a rate of 2.5ft^3 per minute.

4 0
3 years ago
Worth 50 points PLUS I'll give the person who answers FIRST and BEST the brainlest answer.
WARRIOR [948]
Okay, this is not really an answer, but I think in 2020, we will be in the 20 trillions. O know that is not the answer you were looking for, but its all I got.
4 0
3 years ago
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