In Exercises 5-8, which of the given subsets of P₂ are subspaces of P₂? 5. W {p(x) in P₂: p(0) + p(2)=0} 6. W {p(x) in P₂: p(1) = p(3)} 7. W = {p(x) in P₂: p(1) p(3)=0} 8. W {p(x) in P₂: p(1) = -p(-1)}
In Exercises 5-8, which of the given subsets of P₂ are subspaces of P₂? 5. W {p(x) in P₂: p(0) + p(2)=0} 6. W {p(x) in P₂: p(1) = p(3)} 7. W = {p(x) in P₂: p(1) p(3)=0} 8. W {p(x) in P₂: p(1) = -p(-1)}
In Exercises 5-8, which of the given subsets of P₂ are subspaces of P₂? 5. W {p(x) in P₂: p(0) + p(2)=0} 6. W {p(x) in P₂: p(1) = p(3)} 7. W = {p(x) in P₂: p(1) p(3)=0} 8. W {p(x) in P₂: p(1) = -p(-1)}
Linear algebra: please solve last 3 parts 6, 7 and 8 correctly and handwritten
Transcribed Image Text:In Exercises 5-8, which of the given subsets of P₂ are
subspaces of P₂?
5. W = {p(x) in P₂: p(0) + p(2)=0}
6. W = {p(x) in P₂: p(1) = p(3)}
7. W = {p(x) in P₂: p(1)p(3) = 0}
8. W {p(x) in P₂: p(1) = -p(-1)}
=
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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