Estimate the product. Then find the exact product.
2 answers:
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So we are given the system:
Written in matrix form we get:
![\left[\begin{array}{cc}2&4\\6&3\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}8\\-3\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C6%263%5Cend%7Barray%7D%5Cright%5D%20%0A%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20)
We compute the solution like this:
![ \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}2&4\\6&3\end{array}\right] ^{-1} \left[\begin{array}{c}8\\-3\end{array}\right] \\= \left[\begin{array}{cc}-3&4\\6&-2\end{array}\right] \left[\begin{array}{c}8\\-3\end{array}\right] \dfrac{1}{18}\\= \left[\begin{array}{c}2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%20%0A%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%0A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C6%263%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3%264%5C%5C6%26-2%5Cend%7Barray%7D%5Cright%5D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20%5Cdfrac%7B1%7D%7B18%7D%5C%5C%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
The solution is :
![\left[\begin{array}{c}2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
Written in matrix form we get:
We compute the solution like this:
The solution is :