3x+2y-z =-1

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.

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.