Answer:41550
Step-by-step explanation:
30000×.07=2100
2100×5.5=11550
11550+30000=41550
Answer:
9 total
2/9 - 5/9 -2/9 so 3 i guess...
Step-by-step explanation:
Answer:
(a)First Row, First Column =1
(b)First Row, second Column =0
(c)Second Row, First Column =0
(d)Second Row, second Column =1
Step-by-step explanation:
Given matrix ![M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)](https://tex.z-dn.net/?f=M%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-5%263%5C%5C-8%265%5Cend%7Barray%7D%5Cright%29)
The Inverse of a 2X2 matrix
![A=\left(\begin{array}{ccc}a&b\\c&d\end{array}\right)](https://tex.z-dn.net/?f=A%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%29)
can be found using the following:
![A^{-1}=\dfrac{1}{ad-bc} \left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7Bad-bc%7D%20%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5Cend%7Barray%7D%5Cright%29)
Therefore:
![M^{-1}=\dfrac{1}{(5*-5)-(3*-8)} \left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=-1\left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)](https://tex.z-dn.net/?f=M%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7B%285%2A-5%29-%283%2A-8%29%7D%20%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D5%26-3%5C%5C8%26-5%5Cend%7Barray%7D%5Cright%29%5C%5C%3D-1%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D5%26-3%5C%5C8%26-5%5Cend%7Barray%7D%5Cright%29%5C%5C%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-5%263%5C%5C-8%265%5Cend%7Barray%7D%5Cright%29)
Next, we find the product ![M^{-1}M](https://tex.z-dn.net/?f=M%5E%7B-1%7DM)
![M^{-1}M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\\=\left(\begin{array}{ccc}-5*-5+3*-8&-5*3+3*5\\-8*-5+5*-8&-8*3+5*5\end{array}\right)\\=\left(\begin{array}{ccc}1&0\\0&1\end{array}\right)](https://tex.z-dn.net/?f=M%5E%7B-1%7DM%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-5%263%5C%5C-8%265%5Cend%7Barray%7D%5Cright%29%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-5%263%5C%5C-8%265%5Cend%7Barray%7D%5Cright%29%5C%5C%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-5%2A-5%2B3%2A-8%26-5%2A3%2B3%2A5%5C%5C-8%2A-5%2B5%2A-8%26-8%2A3%2B5%2A5%5Cend%7Barray%7D%5Cright%29%5C%5C%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%29)
Therefore:
(a)First Row, First Column =1
(b)First Row, second Column =0
(c)Second Row, First Column =0
(d)Second Row, second Column =1
NOTE: The multiplication of a matrix and its inverse always gives the identity matrix as seen above,