2 Matrix problems?

[inso]

How do u think those are solved?
x-2y+2z=4
x-y =-2
2x-3y+2z=2
3x-4y+a.z=0

And
A= 2 1 B= 2 -1
3 1 -3 -1
Solve:
a)X+B=3(A-X)
b)AX-X=AB-B
c) YA+Y=AB+B

 

[Denis]

How do u think those are solved?

Solve them the way you were taught in class.

And "u" is not a word; use "you".

 

[stapel]

How do u think those are solved?

To learn how to solve systems of linear equations, try some online lessons. :wink:

 

[soroban]

Hello, inso!

I'll get you started on the second one . . .

\(\displaystyle \text{Given: }\;A \:=\:\begin{pmatrix}2&1\\3&1\end{pmatrix} \quad B \:=\:\begin{pmatrix}2&\text{-}1\\\text{-}3&\text{-}1\end{pmatrix}\)

\(\displaystyle \text{Solve: }\;(a)\;\;X+B\:=\:3(A-X)\)

\(\displaystyle \text{We have: }\;X + B \:=\:3(A - X) \quad\Rightarrow\quad X + B \:=\:3A - 3X\)

. . . . \(\displaystyle 4X \:=\:3A - B \quad\Rightarrow\quad X \:=\:\tfrac{1}{4}(3A - B)\)


\(\displaystyle \text{Then we have: }\;X \;=\;\tfrac{1}{4}\left[3\begin{pmatrix}2&1\\3&1\end{pmatrix} - \begin{pmatrix}2&\text{-}1\\\text{-}3&\text{-}1\end{pmatrix} \right] \;=\;\tfrac{1}{4}\left[\begin{pmatrix}6&3\\9&3\end{pmatrix} - \begin{pmatrix}2&\text{-}1\\\text{-}3&\text{-}1\end{pmatrix}\right]\)


. . .\(\displaystyle \text{Therefore: }\;X \;=\;\tfrac{1}{4}\begin{pmatrix}4&4\\12&4\end{pmatrix} \;=\;\begin{pmatrix} 1&1\\3&1\end{pmatrix}\)