Stability of the E8-form (Ex)

Show an isometry of unimodular forms

$\langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle -1 \rangle \cong ({\mathbb Z}^8,\lambda) \oplus \langle -1 \rangle$$<wikitex>; Show an isometry of unimodular forms $\langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle -1 \rangle \cong ({\mathbb Z}^8,\lambda) \oplus \langle -1 \rangle$ </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]\langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle 1 \rangle \oplus \langle -1 \rangle \cong ({\mathbb Z}^8,\lambda) \oplus \langle -1 \rangle$