i have matrix A and C how can i find the relation between element of matrix B? A*B=C

hello every one i have 3 different matrix such as A=[a b;c d] and B=[X1;X2] and C=[K;K2] then A*B=C how can i find i find the relation between element of matrix B? can you explain thank you

Answer 1

[Star Strider]

I’m letting the Symbolic Math Toolbox do this for me this morning:

syms a b c d X1 X2 K1 K2 
A=[a b;c d];
B=[X1;X2];
C=[K1;K2];
Eqn = A*B == C;
[X1,X2] = solve(Eqn, B)

X1 = 
-(K2*b - K1*d)/(a*d - b*c)

X2 = 
(K2*a - K1*c)/(a*d - b*c)

[amina shafanejad]

i have one question if we have value for A and C still we use same method or different method? thank you

[Star Strider]

Essentially the same method, although if you have numbers in the ‘A’ matrix and ‘C’ vector, use the backslant (\) operator (or the mldivide function) instead:

B = A\C

That also works in the Symbolic Math Toolbox:

syms a b c d X1 X2 K1 K2 
A=[a b;c d];
B=[X1;X2];
C=[K1;K2];
B = A\C

B =

   -(K2*b - K1*d)/(a*d - b*c)
    (K2*a - K1*c)/(a*d - b*c)

[amina shafanejad]

thanks for your response, i tried ur solution i have one more question because my result matrix i mean C is zeros matrix of (2,1) it give me 0 to result of X1 and X2 is it any way we find this in relation way such as X2=5X1 for example if we input value for matrix a can u help me with that? thank you

[Star Strider]

My pleasure.

If C is [0; 0] (that is, ‘K1’ and ‘K2’ are both 0), then ‘B’ will also be [0; 0] regardless of whatever ‘A’ is (unless it is also a zeros matrix, in which instance ‘B’ will be [NaN; NaN].)

If both [X1; X2] are [0; 0], then of course X2=5*X1.

[amina shafanejad]

thank you so by using the equation in above you write i can get some answer like X1=5X2 i mean or this is impossible to do in matlab?

[Star Strider]

I am not certain that I understand what you want to do. If you want to solve for ‘C’ such that X1=5*X2 you can do that with the Symbolic Math Toolbox.

[amina shafanejad]

actually my matrix a and c has value but my matrix b has variable such matrix a is [1 2;3 5] and matrix c is zeros matrix of (2,1) i want to see the relation between the element of matrix b such as for example 2X1=5X2 and the main equation is a*b=c? is there any command in matlab help me with that?

[Walter Roberson]

b = a\c when a and c are both numeric.

However, the special case of a*b = 0 is known as finding the "null space" of a matrix, and finding the "null vectors". You should see the null() routine for that. There are special processes for finding those; the \ command can only come up with one of them, and will usually come up with a 0 vector which is the trivial answer. null() is used to find the general solution for the null space. There are a number of uses for finding the solutions to a*b=0, and it is something to look into specially.