Respuesta :

luantonicelli

Answer:

(x,y,z)=(2,0,-4)

Step-by-step explanation:

  • First we create the extended matrix from the equations

[tex]\left[\begin{array}{ccc|c}2&2&-3&16\\2&-3&2&-4\\4&-1&3&-4\end{array}\right][/tex]

Using the elementary operations

  • Substract to the 2nd line the first one, and the 3rd one twice the first:

[tex]\left[\begin{array}{ccc|c}2&2&-3&16\\0&-5&5&-20\\0&-5&9&-36\end{array}\right][/tex]

  • Divide the first line by 2, the 2nd one by -5 and substract to the 3rd the 2nd:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&-1&4\\0&0&4&-16\\\end{array}\right][/tex]

  • Divide the 3rd by 4:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&-1&4\\0&0&1&-4\\\end{array}\right][/tex]

  • Add the 3rd to the 2nd:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&0&0\\0&0&1&-4\\\end{array}\right][/tex]

  • Substract the 2nd to the 1st

[tex]\left[\begin{array}{ccc|c}1&0&-3/2&8\\0&1&0&0\\0&0&1&-4\\\end{array}\right][/tex]

  • Add the 3rd multiplied by 3/2:

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

The answer is determined:

x=2

y=0

z=-4

You can check they are correct, by entering in the original formulas.

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