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anzhelika [568]
2 years ago
6

Use a matrix to solve the system:

Mathematics
1 answer:
Romashka-Z-Leto [24]2 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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Points A, B, and C are collinear. Point B is between A and C. BC=8x+709. AB=487+5x. AC=91. Find BC.
Zolol [24]

Answer:

<h3>            BC = 29</h3>

Step-by-step explanation:

Point B is between A and C and the points A, B, and C are collinear so:

AB + BC = AC

487 + 5x + 8x + 709 = 91

  13x + 1196 = 91

       - 1196      - 1196

   13x  =  - 1105

     ÷13     ÷13

    x = - 85

BC =  8x + 709 = 8(-85) + 709 = - 680 + 709 = 29

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3 years ago
Review the proof.A 2-column table with 5 rows. Column 1 is labeled step with entries 1, 2, 3, 4, 5. Column 2 is labeled Statemen
mariarad [96]
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2 years ago
Hey guys! Need help asap! Pls help! Will give brainliest!!!
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Answer:

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