Question 1122192
<pre>
Use your TI-83 or 84 calculator. Use 2ND x<sup>-1</sup>
to access the matrix capability.

Enter this as a 3x5 matrix:

{{{(matrix(3,6,

1, -1,  5, -3, "|", 23.2,
1,  4, -7, -2, "|", 45.6,
3, -5,  7,  4, "|", 29.8))}}}

Press 2ND x<sup>-1</sup>
Press Right arrow   (to highlight MATH)
Press Up arrow 5 times to highlight B:rref(
Press ENTER
Press 2ND x<sup>-1</sup>
Press 1
Type a right parenthesis
Press ENTER
Read this rounded to three decimal places:

{{{(matrix(3,6,

1, 0, 0, -0.528, "|", 23.411,
0, 1, 0, -4.111, "|", 18.244,
0, 0, 1, -2.139, "|",  7.256))}}}

Interpret that as:

{{{matrix(3,1,

1x[1]+0x[2]+0x[3]-0.528x[4]=23.411,
0x[1]+1x[2]+0x[3]-4.111x[4]=18.244,
0x[1]+0x[2]+1x[3]-2.139x[4]=7.256)}}}

Simplify as

{{{matrix(3,1,

x[1]-0.528x[4]=23.411,
x[2]-4.111x[4]=18.244,
x[3]-2.139x[4]=7.256)}}}

Solve for the x's

{{{matrix(3,1,

x[1]=23.411+0.528x[4],
x[2]=18.244+4.111x[4],
x[3]=7.256+2.139x[4])}}}

Replace the x<sub>4</sub>'s by t

{{{matrix(3,1,

x[1]=23.411+0.528t,
x[2]=18.244+4.111t,
x[3]=7.256+2.139t)}}}

Edwin</pre>