partition a matrix to small matrix for find variable

Question

1.

how can find vaiable $y_1,y_2,b_1,b_2$?

How the first matrix divided into smalle matrix$(4*x)$.

The second matrix is then multiplied.

So that the value of variable obtained.

2.

how can do this with matlab?

3.

What is the name of this action?

Answer 1

To find values $y_1,y_2,b_1,b_2$ you should solve following system of four equations in four unknowns :

$$\begin{cases} y_1+y_2+9+16=100 \\ 5y_1+6y_2+21+32=200 \\ 9y_1+10y_2+33+48=b_1 \\ y_1+4y_2+9+4=b_2 \end{cases}$$

Answer 2

I don't know what you mean by $4*x \mid x > 0$, but you can divide the matrix into blocks as $$\left[\begin{array}{@{}cc|cc@{}}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ \hline 9 & 10 & 11 & 12 \\ 1 & 4 & 3 & 1\end{array}\right]\begin{bmatrix}y_1 \\ y_2 \\ 3 \\ 4\end{bmatrix} = \begin{bmatrix}100 \\ 200 \\ b_1 \\ b_2\end{bmatrix}$$ so that you get $$\begin{array}{ccccc} \begin{bmatrix}1 & 2 \\ 5 & 6\end{bmatrix}\begin{bmatrix}y_1 \\ y_2\end{bmatrix} &+& \begin{bmatrix}3 & 4 \\ 7 & 8\end{bmatrix}\begin{bmatrix}3 \\ 4\end{bmatrix} &=& \begin{bmatrix}100 \\ 200\end{bmatrix} \\ \begin{bmatrix}9 & 10 \\ 1 & 4\end{bmatrix}\begin{bmatrix}y_1 \\ y_2\end{bmatrix} &+& \begin{bmatrix}11 & 12 \\ 3 & 1\end{bmatrix}\begin{bmatrix}3 \\ 4\end{bmatrix} &=& \begin{bmatrix}b_1 \\ b_2\end{bmatrix} \end{array}$$ which you can then rearrange to bring all the unknowns to the left-hand side and solve the system.

Answer 3

[1 2 3 4] [$y_1$ $y_2$ 3 4]$^t$ =100 & [5 6 7 8] [$y_1$ $y_2$ 3 4]$^t$ =200

then $y_1=-39$ & $y_2=57 $

also [9 10 11 12] [-39 57 3 4]$^t$=[100 200 $b_1$ $b_2$] & [1 4 3 1] [-39 57 3 4]$^t$=[100 200 $b_1$ $b_2$]

then $b_1=300$ $b_2=202$

I computed it with matlab.