Reference no: EM131013541
We know that the space R2 is two-dimensional. Mathematically, this means that we can generate any vector in R2 using two base vector. For example, any vector in R2 can be written as a weighted sum of i end j, is for same m, n ∈ R, v = mi + nj, where v is an arbitrary 2D vector. These base vectors are not unique. For this problem, we investigate whether or not a= (1, 1) and B = (1, -1) form base vectors,
(a) Consider a vector v = (-3, 4). Find the vector projection of v onto a and b respectively, denote them by projav, and projbv.
(b) For any vector v = (x, y) where x and y are some real numbers, find its vector projection on a and b, and show that
v = projav + projbv.
Show that R2 can be also spanned by a and b, i.e. for any vector v we have v = ma+ nb for some real numbers m and n.
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: We know that the space R2 is two-dimensional. Consider a vector v = (-3, 4). Find the vector projection of v onto a and b respectively, denote them by projav, and projbv.
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