Typo: Proof PEEF, second paragraph, insert "product" (Anna Dovzhik)

Typo: Solution MO.T13 "1<=i<=n" to "1<=j<=n" (Anna Dovzhik)

Typo: Solution MISLE.C27 space in "at" (Jenna Fontaine)

+Typo: Sage MISLE, nonexistent "CINMN" acronym to "CINM" (Bruno Mello)

<sageadvice acro="MISLE" index="matrix inverse, system of equations">

<title>Matrix Inverse, Systems of Equations</title>

-We can use the computational method described in this section in hopes of finding a matrix inverse, as <acroref type="theorem" acro="CINMN" /> gets us halfway there. We will continue with the matrix from <acroref type="example" acro="MI" />. First we check that the matrix is nonsingular so we can apply the theorem, then we get <q>half</q> an inverse, and verify that it also behaves as a <q>full</q> inverse by meeting the full definition of a matrix inverse (<acroref type="definition" acro="MI" />).

+We can use the computational method described in this section in hopes of finding a matrix inverse, as <acroref type="theorem" acro="CINM" /> gets us halfway there. We will continue with the matrix from <acroref type="example" acro="MI" />. First we check that the matrix is nonsingular so we can apply the theorem, then we get <q>half</q> an inverse, and verify that it also behaves as a <q>full</q> inverse by meeting the full definition of a matrix inverse (<acroref type="definition" acro="MI" />).

<input>A = matrix(QQ, [[ 1, 2, 1, 2, 1],