There are 26 letters in the english alphabet, asussuming that they are all upper case, you would multiply 26×6 to find all of the different combinations of numbers.
there are 1000 possible ways to organize the nine individual numbers (000, 001, 002,...,999)
I hope that helps, I am not really sure how you would go on from there, good luck!
The given matrix equation is,
.
Multiplying the matrices with the scalars, the given equation becomes,
![\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%269%5C%5C12%266%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%264y%5C%5C3y%262y%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20)
Adding the matrices,
![\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%2By%269%2B4y%5C%5C12%2B3y%266%2B2y%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20)
Matrix equality gives,
![1.5x+y=z\\ 9+4y=z\\ 12+3y=6z\\ 6+2y=2](https://tex.z-dn.net/?f=%201.5x%2By%3Dz%5C%5C%209%2B4y%3Dz%5C%5C%2012%2B3y%3D6z%5C%5C%206%2B2y%3D2%20)
Solving the equations together,
![y=-2\\ 3y-1.5x=9\\ -1.5x=9+6\\ x=-10](https://tex.z-dn.net/?f=%20y%3D-2%5C%5C%203y-1.5x%3D9%5C%5C%20-1.5x%3D9%2B6%5C%5C%20x%3D-10%20%20)
We can see that the equations are not consistent.
There is no solution.
I need more information to answer this
The answer is d I think but idk