Question 348226
Please help me solve this equation:
Express each of the following systems of equations in the standard multiplicative form {{{ Ax=B }}} and in the augmented matrix form.
a)
<pre>
 {{{system(2w-x-y+2z=3, 
    w+2x-2y+z=1, 
    w+y-2z=0, 
   3w-x-2z=-2)}}}

We'll find the augmented matrix first:

Put in all the 1 or -1 coefficients where the coefficient is 
understood.

Put in 0 coefficients for x in the third equation and for y in the
4th equation.

 {{{system(2w-1x-1y+2z=3, 
    1w+2x-2y+1z=1, 
    1w+0x+1y-2z=0, 
   3w-1x+0y-2z=-2)}}}

Erase all the letters and replace the equal signs by a verticle bar
and put parentheses around the whole thing:

 {{{(matrix(4,6,

2,-1,-1,+2,"|",3, 
1,+2,-2,+1,"|",1, 
1,+0,+1,-2,"|",0, 
3,-1,+0,-2,"|",-2))}}}

That's the augmented matrix.

-----------------------------------------------------

To find the AX=B equation

Matrix A is the 4x4 matrix of coefficients
the numbers left of the bar in the augmented matrix:

 {{{A=(matrix(4,4,

2,-1,-1,+2, 
1,+2,-2,+1, 
1,+0,+1,-2, 
3,-1,+0,-2))}}}

The matrix X is the 4x1 matrix of letters,
(unknowns or variables), in the same order
they appear in the original system of 
equations:

{{{X=(matrix(4,1,w,x,y,z))}}}

The matrix B is the 4x1 matrix of numbers that
appear on the right of the equal signs,  and
right of the bar in the augmented matrix:

{{{B=(matrix(4,1,3,1,0,-2))}}}

So the equation {{{AX=B}}} is

 {{{(matrix(4,4,

2,-1,-1,+2, 
1,+2,-2,+1, 
1,+0,+1,-2, 
3,-1,+0,-2))(matrix(4,1,w,x,y,z))=(matrix(4,1,3,1,0,-2))}}} 

You do the other one.  It's the same way.  Just follow the same
steps as above.

Edwin</pre>