Write #−5x + 3y + 6z =4# into the first row of an augmented matrix:
#[
(−5, 3, 6, |, 4)
]#
Add #−3x + y + 5z = −5# to the second row of the augmented matrix:
#[
(−5, 3, 6, |, 4),
(−3, 1, 5,|, −5)
]#
Add #−4x + 2y + z = 13# to the third row of the augmented matrix:
#[
(−5, 3, 6, |, 4),
(−3, 1, 5,|, −5),
(−4, 2, 1, |, 13)
]#
Subtract row 2 from row 1:
#[
(−2, 2, 1, |, 9),
(−3, 1, 5,|, −5),
(−4, 2, 1, |, 13)
]#
Subtract row 3 from row 1:
#[
(2, 0, 0, |, -4),
(−3, 1, 5,|, −5),
(−4, 2, 1, |, 13)
]#
Divide row 1 by 2:
#[
(1, 0, 0, |, -2),
(−3, 1, 5,|, −5),
(−4, 2, 1, |, 13)
]#
Multiply row 1 by 3 and add to row 2:
#[
(1, 0, 0, |, -2),
(0, 1, 5,|, -11),
(−4, 2, 1, |, 13)
]#
Multiply row 1 by 4 and add to row 3:
#[
(1, 0, 0, |, -2),
(0, 1, 5,|, -11),
(0, 2, 1, |, 5)
]#
Multiply row 2 by -2 and add to row 3:
#[
(1, 0, 0, |, -2),
(0, 1, 5,|, -11),
(0, 0, -9, |, 27)
]#
Divide row 3 by -9:
#[
(1, 0, 0, |, -2),
(0, 1, 5,|, -11),
(0, 0, 1, |, -3)
]#
Multiply row 3 by -5 and add to row 2:
#[
(1, 0, 0, |, -2),
(0, 1, 0,|, 4),
(0, 0, 1, |, -3)
]#
