## anonymous one year ago Need genius math people's help !!!!! There are two matrices A and B. A = 4 -6 B= 5 1 4 -2 -1 -3 I want to find a matrix D which satisfies A+B+D=I and I got below the answer but it said still wrong. -8 5 -3 6 Please help me people !!!!!!!!!!!!!!!!!

1. sdfgsdfgs

I= 1 1 1 1 right? if so, then -8 and 6 are right, re-calculate the other two.

2. anonymous

Isn't I = 1 0 0 1 ???

3. UsukiDoll

yes a 2 x 2 identity matrix is 1 0 0 1

4. UsukiDoll

hmmm latex for matrices is nasty.. so we have this equation A+B+D=I where A and B matrices are given. so we need to find Matrix D

5. sdfgsdfgs

@taejunlee sorry u are right of cuz...been a while since i looked at matrix. so ur ans should be right then. may be someone else can help u. good luck! :)

6. UsukiDoll

what if we rearrange this equation for a bit D =I-A-B like that and then use matrix addition and matrix subtraction ?

7. UsukiDoll

|dw:1437187726707:dw|

8. UsukiDoll

now use matrix subtraction. @taejunlee

9. UsukiDoll

blah...... we can start with the first two matrices and then that result - matrix B

10. UsukiDoll

|dw:1437188093151:dw|

11. anonymous

so isn't answer -8 6 -2 6 ???

12. UsukiDoll

well let's check first... could you do the matrix in black (the one I drew) ?

13. anonymous

that is -3 6 -4 3

14. UsukiDoll

excellent now we just need to do matrix subtraction with matrix b hold on a sec .. need to draw

15. UsukiDoll

|dw:1437188427336:dw|

16. anonymous

and -8 5 -3 6....

17. UsukiDoll

which is the matrix you got in the first place... it should be right then. Why is it wrong?

18. anonymous

well.. that was what I thought.. I better ask professor ..

19. UsukiDoll

|dw:1437188557694:dw|

20. UsukiDoll

that should end up to 1 0 0 1

21. UsukiDoll

you got the right matrix. It must be some bug in the online homework or the professor's stupidity or something

22. UsukiDoll

|dw:1437188718111:dw|

23. UsukiDoll

|dw:1437188725475:dw|

24. anonymous

guess there is something wrong with online system.. anyways I really appreciate what you've done for me :)

25. UsukiDoll

hahah no problem :)

26. sdfgsdfgs

@taejunlee only thing i can think of is check the + signs in ur eqn n see if one may be a - instead.

27. UsukiDoll

@sdfgsdfgs he got the right matrix, so it wasn't the equation. It's some bug in his online stuff.

28. sdfgsdfgs

@UsukiDoll u are probably right - was just thinking may be the eqn should be A+B-D=I or something like that instead.

29. Empty
30. UsukiDoll

^ matrix in latex is crummy, but thanks for the link. still I prefer to draw in this case.

31. UnkleRhaukus

\begin{align} \textbf A+\textbf B+\textbf D &=\textbf I\\[2ex] \begin{pmatrix}4&-6\\4&-2\end{pmatrix} +\begin{pmatrix}5&1\\-1&-3\end{pmatrix} +\begin{pmatrix}d_{00}&d_{01}\\d_{10}&d_{11}\end{pmatrix} &=\begin{pmatrix}1&0\\0&1\end{pmatrix}\\[2ex] \begin{pmatrix}4+5&-6+1\\4-1&-2-3\end{pmatrix} +\begin{pmatrix}d_{00}&d_{01}\\d_{10}&d_{11}\end{pmatrix} &=\begin{pmatrix}1&0\\0&1\end{pmatrix}\\[2ex] \begin{pmatrix}9&-5\\3&-5\end{pmatrix} +\begin{pmatrix}d_{00}&d_{01}\\d_{10}&d_{11}\end{pmatrix} &=\begin{pmatrix}1&0\\0&1\end{pmatrix}\\[2ex] \begin{pmatrix}d_{00}&d_{01}\\d_{10}&d_{11}\end{pmatrix} &=\begin{pmatrix}1&0\\0&1\end{pmatrix}-\begin{pmatrix}9&-5\\3&-5\end{pmatrix}\\[2ex] \begin{pmatrix}d_{00}&d_{01}\\d_{10}&d_{11}\end{pmatrix} &=\begin{pmatrix}1-9&0+5\\0-3&1+5\end{pmatrix}\\[2ex] \textbf D &=\begin{pmatrix}-8&5\\-3&6\end{pmatrix} \end{align}

32. UsukiDoll

wow that looks nice.

33. UnkleRhaukus

$\begin{bmatrix}\circ&&\circ\\&\angle\\&\smile\end{bmatrix}$