Systems of Linear Equations

Can someone please help me solve these:

1. by using Gauss-Jordan elimination in matrix form to solve the system

w+x+3y-2z =0
2w+3x+y-2x=9
3w+5x+13y-9z=1
-2w+x - z =0

2. For what values of the parameter a does the following system of equations have a solution?

6x+y=7
3x+y=4
-6x-2y=a

Reply 1

gilyan

Original Matrix
w x y z
1 1 3 -2 0
2 3 1 -2 9
3 5 13 -9 1
-2 1 0 -1 0
--------------------------------------------------------
set r1 w:1, use r1 to set w:0 for r2-r4
1 1 3 -2 0
0 1 -5 2 9 r2-2r1
0 2 4 -3 1 r3-3r1
0 3 6 -5 0 r4+2r1
--------------------------------------------------------
set r2 x:1, use r2 to set x:0 for r1,3,4
1 0 8 -4 -9 r1-r2
0 1 -5 2 9
0 0 14 -7 -17 r3-2r2
0 0 21 -11 -27 r4-3r2
------------------------------------------------------------
set r3 y:1, use r3 to set y:0 for r1,2,4
1 0 0 0 0.714285 r1-8r3
0 1 0 -0.5 2.928571 r2+5r3
0 0 1 -0.5 -1.21428
0 0 0 -0.5 -1.5 r4-21r3
-------------------------------------------------------------
set r4 z:1, use r4 to set z:0 for r1-3
1 0 0 0 0.714285 r1
0 1 0 0 4.428571 r2+0.5r4
0 0 1 0 0.285714 r3+0.5r4
0 0 0 1 3
Read answers (changed to fractions)
w=5/7 Check 0 eqn1
x=4 3/7 Check 9 eqn2
y=2/7 Check 1 eqn3
z=3 Check 0 eqn4

Reply 2

doddyz

oh my god! r u clever r am i jus dumb! lol

Reply 3

Unregistered

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