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anzhelika [568]
3 years ago
6

Use a matrix to solve the system:

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\

Rewrite these equations in matrix form

\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\

we can write it like this,

AX=B\\X=A^{-1}B

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]  \\

now multiply the matrix with B

X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\

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Are these two answers correct??
Damm [24]

Answer:

Yes

Step-by-step explanation:

7 0
3 years ago
PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.
Umnica [9.8K]

Answer:

D. 70.34 cm^2

Step-by-step explanation:

Area of sector of a circle is given as θ/360*πr²

Where,

r = radius = 12 cm

θ = 56°

Use 3.14 as π

Plug in the values into the formula and solve

area = \frac{56}{360}*3.14*12^2

area = 70.34

Area of the sector ABC = 70.34 cm^2

The answer is D

4 0
3 years ago
Find the quotient simplify your answers a+3 over a divided by 8 over a
mihalych1998 [28]
ANSWER

\frac{a + 3}{8}



EXPLANATION

We want to simplify

\frac{a + 3}{a}  \div  \frac{8}{a}


We multiply the first fraction by the reciprocal of the second fraction to obtain,



\frac{a + 3}{a}   \times  \frac{a}{8}


We cancel the common factors to get,


\frac{a + 3}{1}   \times  \frac{1}{8}

This gives us,

\frac{a + 3}{8}
4 0
3 years ago
Write 0.0000004954 in scientific notation.
SCORPION-xisa [38]
By scientific notation I am assuming you mean standard form, as that is used primarily in scientific calculations. The answer in standard form would be
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I hope this helps!

4 0
3 years ago
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I need help with this question. 12 points
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There is no question
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