Answer:
The solution of the system of equations is, (1,-1,2)
Step-by-step explanation:
Given system equation;
x + 5y - 3z = -10
-5x + 6y – 5z = -21
-x + 8y - 8z = -25
Matrix form is written as;
![\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%265%26-3%5C%5C-5%266%26-5%5C%5C-1%268%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C6%26-5%5C%5C8%26-8%5Cend%7Barray%7D%5Cright%5D%20-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%5D%20-3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%28-8%29%20-5%2835%29-3%28-34%29%3D%20-8%20-%20175%2B%20102%20%3D%20-81)
Cofactor;
![First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\](https://tex.z-dn.net/?f=First%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%206%26-5%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%20-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5B-8%20%20%5C%20%5C%20-35%20%5C%20%5C%20-34%5D%5C%5C%5C%5C%5C%5C%5C%20Second%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%205%26-3%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%201%26-3%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C1%265%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5B16%5C%20%5C%20-11%20%5C%20%5C%20-13%5D%5C%5C%5C%5C%5C%5C)
![Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]](https://tex.z-dn.net/?f=Third%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%205%26-3%5C%5C%5C%206%26-5%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%201%26-3%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C1%265%5C%5C-5%266%5Cend%7Barray%7D%5Cright%5D%3D%20%5B-7%20%5C%20%20%5C%2020%5C%20%5C%2031%5D)
![\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26-35%26-34%5C%5C16%26-11%26-13%5C%5C-7%2620%2631%5Cend%7Barray%7D%5Cright%5D)
![inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=inverse%20%5C%20matrix%20%3D-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
Solution of the matrix:
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-8%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B16%2A-21%20%7D%7B-81%20%7D%20%2B%20%5Cfrac%7B-7%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-35%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B-11%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B20%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-34%2A-10%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B-13%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B31%2A-25%20%7D%7B-81%20%7D%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B-162%7D%7B-81%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Therefore, the correct option is (1,-1,2)
Answer:
-5, 4.1, 4.7, 16 squared
Step-by-step explanation:
negative numbers are always the least, then 4.1 is less than 47/10 which is 4.7 and 16 squared which is 256, then we have 4.7 because that is less than 256 which is the greatest number.
The question is asking to calculate the said coordinates and determine if it is a right triangle or not and state the evidence why and in my own calculation and further understanding about the said coordinates, I would say that its not and the Z coordinates should be (6,1). Hope this would help
Step-by-step explanation:
Finding surface area
To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for area of the base of the prism, p stands for the perimeter of the base, and h stands for the height of the prism. Since this is a triangular prism, substitute the area formula of a triangle for B.
Is this multiplying or what??? Anyways try calculating those numbers so basically you need to calculate 28x2 or if you have to divide them or multiply them you would get the answer is very simple
