General Vector Spaces
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Question: Let W be the space spanned by f = sinx and g = cosx.
(a) Show that for any value of theta, f, = sin(x + theta) and g_1 = cos (x + theta) vectors in W.
(b) Show that f_1 and g_1 form a basis for W.
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Solution Summary
In about 180 words, this solution discusses the two proofs regarding vector spaces. The solution is brief, but concise and will be understandable for anyone with a basic understanding of this subject material.
Solution Preview
Because f = sin x and g = cos x span the vector space S, any linear or multiplicative combination of these two vectors will also be vectors in W.
Consider u=sin(x+theta) and v=cos(x+theta)
By trigonometric identities,
Then, u = sinx ...
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