Let L: R4 R be a linear transformation for which L(4) = 0. Let H be...

 

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Let L: R4 R be a linear transformation for which L(4) = 0. Let H be the hyperplane determined by w = 0 (the variables we use in R are x, y, z, w). Prove using the definition that the subset L(H) R is a subspace. Discuss how to determine its dimension. Let L: R4 R be a linear transformation for which L(4) = 0. Let H be the hyperplane determined by w = 0 (the variables we use in R are x, y, z, w). Prove using the definition that the subset L(H) R is a subspace. Discuss how to determine its dimension.

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To prove that LH is a subspace one is supposed to show that it satisfies the three properties of a s... View the full answer