Respuesta :
Answer:
An electronics company can be produce 350 transistors and 340 computer chips, they can´t produce resistors.
Step-by-step explanation:
1. We will name the variables for transistors, resistors and the computer chips.
a = Transistors
b= Resistors
c = Computer chips
2. We propose three linear equations, one for the copper, one for the zinc and one for the glass.
[tex]\left \{ {{3a+3b+2c=1730} \atop {a+2b+c=690}}\atop {2a+b+2c=1380}} \right.[/tex]
3. We write the matrix form as Ax=d
[tex]A=\left(\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right)[/tex]
[tex]x=\left(\begin{array}{ccc}a\\b\\c\end{array}\right)[/tex]
[tex]A=\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)[/tex]
With this formula the solution of x is [tex]x=\frac{d}{A}[/tex] or [tex]x=A^{-1}d[/tex]
4. We will find the inverse matrix [tex]A^{-1}[/tex] using the formula:
[tex]A^{-1} = \frac{1}{detA} (C_{A})^{T}[/tex]
a. det A
[tex]det A=\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right] =3*(4-1)-3*(2-2)+2*(1-4)=9-0-6=3[/tex]
b. [tex](C_{A})^{T}[/tex]
[tex]C_{A}=\left(\begin{array}{ccc}4-1&.(2-2)&1-4\\-(6-2)&6-4&-(3-6)\\3-4&-(3-2)&6-3\end{array}\right)[/tex]
[tex]C_{A}=\left(\begin{array}{ccc}3&.0&-3\\-4&2&3\\-1&-1&3\end{array}\right)[/tex]
[tex](C_{A}) ^T=\left(\begin{array}{ccc}3&0&-3\\-4&2&3\\-1&-1&3\end{array}\right)^T[/tex]
[tex](C_{A}) ^T=\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)[/tex]
c.[tex]A^{-1} [/tex]
[tex]A^{-1}=\frac{1}{3} \left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)[/tex]
5. As [tex]x=\frac{d}{A}[/tex] or [tex]x=A^{-1}d[/tex], the solution of x is:
[tex]x=\frac{1}{3}\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)[/tex]
[tex]x=\frac{1}{3}\left(\begin{array}{ccc}(3*1730)+(-4*690)+(-1*1380)\\(0*1730)+(2*690)+(-1*1380)\\(-3*1730)+(3*690)+(3*1380)\end{array}\right)[/tex]
[tex]x=\frac{1}{3}\left(\begin{array}{ccc}1050\\0\\1020)\end{array}\right)[/tex]
[tex]X=\left[\begin{array}{ccc}350\\0\\340\end{array}\right][/tex]
Therefore:
a= 350 Transistors
b=0 Resistors
c=340 Computer chips
