Use naive Gauss elimination to factor the following system according to the description in Section 10.2:

7x₁ + 2x₂ − 3x₃ = −12
2x₁ + 5x₂ − 3x₃ = −20
x₁ − x₂ − 6x₃ = −26

Then, multiply the resulting [L] and [U] matrices to determine that [A] is produced.