Prove Theorem 1.4. Let h, g: V W be linear maps represented with respect to bases
Question:
Let h, g: V → W be linear maps represented with respect to bases B,D by the matrices H and G and let r be a scalar. Then with respect to B,D the map r ∙ h: V → W is represented by rH and the map h + g: V → W is represented by H + G.
(a) Prove that matrix addition represents addition of linear maps.
(b) Prove that matrix scalar multiplication represents scalar multiplication of linear maps.
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Represent the domain vector V and the maps g h V W with respect to base...View the full answer
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