Answer:
Step-by-step explanation:
Given matrix
![A=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%5C%5C-1%262%5Cend%7Barray%7D%5Cright%5D)
And
![B=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C-2%26k%5Cend%7Barray%7D%5Cright%5D)
We need to find the value of 
, that will make 
.
Let us find 
![AB=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]\times \left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%5C%5C-1%262%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C-2%26k%5Cend%7Barray%7D%5Cright%5D)
![AB=\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2616%2B2k%5C%5C-6%26-4%2B2k%5Cend%7Barray%7D%5Cright%5D)
Now, let us find 
![BA=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]\times \left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]](https://tex.z-dn.net/?f=BA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C-2%26k%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%5C%5C-1%262%5Cend%7Barray%7D%5Cright%5D)
![BA=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]](https://tex.z-dn.net/?f=BA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2612%5C%5C-8-k%26-4%2B2k%5Cend%7Barray%7D%5Cright%5D)
Put
![\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2616%2B2k%5C%5C-6%26-4%2B2k%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2612%5C%5C-8-k%26-4%2B2k%5Cend%7Barray%7D%5Cright%5D)
In order to make , the 
should be equal. As other two values are equal that are 
By solving each equation
And
We can see if the value then
Answer: the shape is a rectangle
Step-by-step explanation:
Simplify by combining the real and imaginary parts of each expression
−3+14i
Well let's see.
If the figure is split up into 10 pieces, then
each piece is 1/10 of the whole figure.
If 2 of the pieces are shaded, then
2/10 of the whole figure is shaded.
How many pieces are left ?
There were 10 pieces all together, and
2 of them are shaded. Hmmm. I think
there are probably (10 - 2) = 8 of them left
that are not shaded.
8 pieces makes 8/10 of the whole figure.
