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ch4aika [34]
3 years ago
11

FURTHER MATHEMATICS Use determinants to solve the systems of equation:

Mathematics
1 answer:
maw [93]3 years ago
8 0

Answer:

Step-by-step explanation:

\left\{\begin{array}{ccc}2x+1y+2z&=&13\\1x+1y-2z&=&8\\1x+2y+1z&=&11\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}2&1&2\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\0&\frac{1}{2}&-3\\0&1&3\end{array}\right| =2*(\frac{3}{2}+3)=9\\\\

\Delta_1=\left| \begin{array}{ccc}13&1&2\\8&1&-2\\11&2&1\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\8&1&-2\\\frac{11}{2}& 1&\frac{1}{2}\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\-5&0&-4\\\frac{-5}{2}& 0&\frac{5}{2}\end{array}\right| \\\\=2*(-1)*(\frac{-25}{2}-\frac{20}{2}) =45\\

\Delta_2=\left| \begin{array}{ccc}2&13&2\\1&8&-2\\1&11&1\end{array}\right| \\\\\\=\left| \begin{array}{ccc}3&21&0\\3&30&0\\1&11&1\end{array}\right| \\\\\\=1*(90-63) =27\\

\Delta_3=\left| \begin{array}{ccc}2&1&13\\1&1&8\\1&2&11\end{array}\right| \\\\\\=\left| \begin{array}{ccc}0&-1&-3\\0&-1&-3\\1&2&11\end{array}\right| \\\\\\=0\\

\left\{\begin{array}{ccc}x=\dfrac{\Delta_1}{\Delta}=\dfrac{45}{9}=5\\\\y=\dfrac{\Delta_2}{\Delta}=\dfrac{27}{9}=3\\\\z=\dfrac{\Delta_3}{\Delta}=\dfrac{0}{9}=0\\\end{array}\right.

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The product of 3 consecutive odd numbers is 3,315. Enter a simplified expression for finding the numbers. Let n be the first odd
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Answer:

n^3+6n^2+8n=3315

Step-by-step explanation:

Let n be the first odd number.

The 2nd consecutive odd number would be n+2 and 3rd consecutive odd number would be n+2+2=n+4.

We have been given that the product of 3 consecutive odd numbers is 3,315. The product of 3 consecutive odd numbers would be n(n+2)(n+4).

Now we will equate the product with 3315 as:

n(n+2)(n+4)=3315    

Let us simplify the left side of equation.

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Now, we will apply FOIL to find the product of left side as:

n^2\cdot n+n^2\cdot 4+2n\cdot n+2n\cdot4=3315

n^3+4n^2+2n^2+8n=3315

n^3+6n^2+8n=3315

Therefore, our required equation would be n^3+6n^2+8n=3315.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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