How To Solve This Simultaneous Equations. 3x + 2y - Z = -1 X - Y + Z = 6 3x + Y + 2z = 15?

2 Answers

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Anonymous answered
3x+2y-z =-1
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Anonymous answered
First,
rearrange the equations.
Write each equation with all unknown
quantities on the left-hand side and all known quantities on the right
side. Thus, for the equations given, rearrange them such that all terms
involving x,
y
and z are
on the left side of the equal sign.Second, write
the equations in a matrix form.
To write the equations in the matrix form Ax
= b,
where x
is the vector of unknowns, you have to arrange the unknowns in vector x,
the coefficients of the unknowns in matrix A
and the constants on the right hand of the equations in vector b.
In this particular example, the unknown column x
=  [x y z]'

the coefficient matrix is

A
= [-6 -2  2
       -3  4 -3
        2  4 -7]

and the known constant column vector is

b
= [15 13 -9]'

Note than the columns of A
are simply the coefficients of each unknown from all the three
expressed equations. The apostrophe
at the end of vectors x
and b
means that those vectors are column vectors, not row ones (it is Matlab
notation).

Third, solve
the simultaneous equations in Matlab.
Enter the matrix A
and vector b,
and solve for vector x
with the instruction 'x = A\b' (note that the '\' sign is different
from the ordinary
division '/'
signThe Matlab answer is:

A =
    -6   
-2     2
   
-3    
4    -3
    
2    
4    -7

b =
    15
    13
    -9

x =  
-2.7273
    2.7727
    2.0909

You can test the result by performing the substitution and multiplying Ax
to get b,
like this:

A*x

And the Matlab answer is:

Ans =
   15.0000
   13.0000
   -9.0000

>>

which corresponds to b,
indeed.

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