#import "/src/lib.typ": *

#let A = mat.mat(
  (3, -3, -1, 2, -9),
  (1, -1, 2, -1, -6),
  (1, -1, 1, 1, -6),
  (-1, 1, -1, -2, 7)
)

#let b = vec.vec(13, -6, 1, -3)

#let A2 = mat.mul-row(A, 2, 3)
#let A3 = mat.div-row(A, 1, 2)
#let A4 = mat.add-row(A, 2, 3, f: 2)

$
  A = #mat.display(A) quad b = #vec.display(b)\
  A_2 = #mat.display(A2)\
  A_3 = #mat.display(A3)\
  A_4 = #mat.display(A4)\
$

#let E = gauss.echelon(A)

$
  E = #mat.display(E)
$

#let M = mat.mat(
  (2, 4, 5, 6),
  (-1, 5, 6, 9),
  (3, 7, 1, -6),
  (4, -2, 3, 5)
)
$M = #mat.display(M)$

#let d = mat.det(M)
$det(M) = #d$

#mat.det-steps(M)