Let W = Span{1, t, t2} which is a subspace of the vector space C[−π, π], the set of all continuous functions defined for t ∈ [−π, π]. For each of the following vectors v, find projW v. Use the inner product (a) v = cos t (b) v = sin t (c) v = et ⟨f,g⟩ =integral π −π f g dt.
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Let W = Span{1, t, t2}
which is a subspace of the vector space C[−π, π], the set of all continuous functions defined for t ∈ [−π, π]. For each of the following vectors v, find projW v. Use the
inner product
(a) v = cos t (b) v = sin t (c) v = et
⟨f,g⟩ =integral π −π f g dt.
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