Expert: Alon Mandes - 10/13/2009

Question
QUESTION: Find the matrix A given ethe equation. please answer me ASAP

ANSWER: Hello Attir,
Let's review a basic fact concerning Matrix equations :
Suppose that A,B %26 C are square matrices, If A*B=C , then
1. B=Inv(A)*C
2. A=C*Inv(B)
Where Inv is the inversion of the matrix.
Now, let's solve our problem :
5*Inv(M)-3*A*Inv(N)=P
Where

Inv(M) = -1     -0.33      2
         0      0       0.33
         0.66   0.33   -1.66

Inv(N) = 0.8    0.2    0.2
        -1     0.2   -0.2
         0     0.2    0

P=       735    630    15
       -210   -120   -30
       -210   -135   -60
so,
-3*A*Inv(N)=P-5*Inv(M)
A*Inv(N)=(1/3)*[5*Inv(M)-P]
A=(1/3)*[5*Inv(M)-P]*Inv(Inv(N))]
A=(1/3)*[5*Inv(M)-P]*N] .
I ran Matlab program %26 got the answer :
A=1.0e+003 *
1.1917    1.2000   -3.4444
-0.0863   -0.1390    0.4253
0.0753   -0.0108    0.1632

Alon.




---------- FOLLOW-UP ----------

QUESTION: hi Mandes, actully ur answer to the question was wrong, however i did the same which u did for solving the answer of the above question but i was wrong again so i just copy the image of my homework site and giving you the question with the right answer and my answer (which was wrong actully), so please figure it out the right one and tell me solution step i will be really great full to you thanks.

Answer
Hi Attir,
Yes, I checked it again %26 I had a mistake in writing the program in Matlab software.
The final %26 correct answer is : A=
5.0279  -92.9507   -8.9905
8.5386   31.9926    4.8999
5.9495   28.0101    3.9899
The answer that you attached is for a different exercise.
Our exercise is : 5Inv(M)-3AInv(N)=P .
The answer you provided was for the exercise : -5AInv(B)+2C=Inv(T) .
I will also solve this this one :
-5AInv(B)+2C=Inv(T)
Where
B= 0.5 1 -0.5
  0  -0.5 0.5
  -1 -4 3.5
C= 135  -310 190
  70 -295  15
  145 -240 70
T= 0  0.2  0.9
  -0.1 -0.3 0
   0  -0.1  -0.4
So,
-5AInv(B)+2C=Inv(T)
-5A+2CB=Inv(T)B
-A=(1/5)[Inv(T)B-2CB]
A=(1/5)[2CB-Inv(T)B]
The answer I got is :
A =

  -7.0000    3.0000    1.0000
  -6.0000   -1.0000    7.0000
   4.0000    8.0000    8.0000

Alon.