Stability of vector bundles (Ex)

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Let E \to X and F \to X be rank k vector bundles over an n-dimensional CW-complex X with k > n.

1) Prove that E is isomorphic to F if and only if E is stably isomorphic to F; i.e. there is an isomorphism E \oplus \underline{\R^i} \cong F \oplus \underline{\R^i} for some i \geq 0, where \underline{\R^i} denotes the trivial rank i bundle over X.

2) If k > n+1, prove that bundle isomorphisms \theta_1, \theta_2 \colon F \to E are fibrewise homotopic if and only if \theta_1 and \theta_2 are stably homotopic; i.e. there is a fibrewise homotopy between \theta_1 \oplus \mathrm{id}_{\underline{\R^i}} and \theta_1 \oplus \mathrm{id}_{\underline{\R^i}} for some i \geq 0.

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