# Pre-Calc

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I have to solve these using matrices by hand. Can someone please help me?

2x-3y-2z=4
(1/4)x-(2/5)y+(3/4)z=(-1/3)
-2x+1.3y-3z=5

Thank you so much! :)

• Pre-Calc -

2x-3y-2z=4
(1/4)x-(2/5)y+(3/4)z=(-1/3)
-2x+1.3y-3z=5
==============================
Google Gauss Jordan reduction

use all integers or fractions
2 -3 -2 4
1/4 -2/5 3/4 -1/3
-2 13/10 -3 5

Divide row 1 by 2
1 -3/2 -1 2
1/4 -2/5 3/4 -1/3
-2 13/10 -3 5

Add (-1/4 * row1) to row2
1 -3/2 -1 2
0 -1/40 1 -5/6
-2 13/10 -3 5

Add (2 * row1) to row3
1 -3/2 -1 2
0 -1/40 1 -5/6
0 -17/10 -5 9

Divide row2 by -1/40
1 -3/2 -1 2
0 1 -40 100/3
0 -17/10 -5 9

Add (17/10 * row2) to row3
1 -3/2 -1 2
0 1 -40 100/3
0 0 -73 197/3

Divide row3 by -73
1 -3/2 -1 2
0 1 -40 100/3
0 0 1 -197/219

Add (40 * row3) to row2
1 -3/2 -1 2
0 1 0 -580/219
0 0 1 -197/219

Add (1 * row3) to row1
1 -3/2 0 241/219
0 1 0 -580/219
0 0 1 -197/219

Add (3/2 * row2) to row1
1 0 0 -629/219
0 1 0 -580/219
0 0 1 -197/219

• Pre-Calc -
• Pre-Calc -

OMG thanks you so much!

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