finding values of a b c d

Hi, Can anyone help me with this. I have no idea how to find the value of a b c d. PLEASE LOOK AT THE PICTURE! THANKS!

[Stephen23]

It is not required to use slow and complex symbolic operations. See Andrei Bobrov's answer for the fast, efficient, and simple numeric solution.

Answer 1

[Birdman]

syms a b c d
eq=[5;-17;14;9]==[2 2 -7 2;3 2 -5 6;9 -8 1 -4;1 5 3 -1]*[a;b;c;d]
sol=solve(eq)
a=vpa(sol.a,4)
b=vpa(sol.b,4)
c=vpa(sol.c,4)
d=vpa(sol.d,4)

[xoxox]

hi, it does not work when i put it in matlab. I am supposed to find the matrix first which is M = [2 3 9 1; 2 2 -8 5; -7 -5 1 3; -2 6 -4 -1]. Then use this M and other w x y z to find out the value of a b c d. but i dont know how to do the second part. Can you please help!

[Birdman]

Well, other way around is to take inverse of the matrix as stated in question and do the following:

syms a b c d
sol=[a;b;c;d]==vpa(inv([2 2 -7 2;3 2 -5 6;9 -8 1 -4;1 5 3 -1])*[5;-17;14;9],4)

By the way, it should work without an error if you have Symbolic Toolbox.

Or, just simply:

inv([2 2 -7 2;3 2 -5 6;9 -8 1 -4;1 5 3 -1])*[5;-17;14;9]

will give you a,b,c and d respectively.

[xoxox]

Yes Thank you!

Answer 2

[Andrei Bobrov]

A = [2  2 -7 -2
     3  2 -5  6
     9 -8  1 -4
     1  5  3 -1];
b = [5;-17;14;9]

abcd = A\b;

[xoxox]

Yes Thank you!