Answer:
![A)\ \ \ \ \left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=A%29%5C%20%5C%20%5C%20%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given the matrix:
, it's inverse is calculated using the formula:
![\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]^{-1}=\frac{1}{det\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] }\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
#Therefore, we calculate as;
![\frac{1}{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] }\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\\#det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] =1\\\\\\\\=\frac{1}{1}\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\=\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%5C%23det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%5C%5C3%268%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D1%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Hence, the inverse of the matrix is ![\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-5%5C%5C-3%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
The first carpenter is 0.4464 of the way is ahead of the second carpenter
<u>Solution:</u>
Given, Two carpenters are building a fence
After 5 minutes, one carpenter is finished 4/7 of the way
Second carpenter finished 1/8 of the way
Now, let us find the work done by each carpenter

Then, extra work done by first carpenter over second carpenter = work done by first carpenter – work done by second carpenter
= 0.5714 – 0.125 = 0.4464
Hence, the 1st carpenter is 0.4464 of the way is ahead of the 2nd carpenter
If you replace 2 with x you will get 1 = 1
This means the anwser is :
x = 2
7^6 is the correct answer