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A hyperplane in n dimensions is a n - 1 dimensional subspace. For instance, a hyperplane in 2-dimensional space can be any liTo check if a vector x is orthogonal to a plane p characterized by 0 and 00, we check whether x = ae for some a E R Ox0 0 x0

A hyperplane in n dimensions is a n - 1 dimensional subspace. For instance, a hyperplane in 2-dimensional space can be any line in that space and a hyperplane in 3-dimensional space can be any plane in that space. A hyperplane separates a space into two sides. In general, a hyperplane in n-dimensional space can be written as 0 01x+0zx2 + '.. + 0nx, = 0. For example, a hyperplane in two dimensions, which is a line, can be expressed as Ax Bx2 + C = 0. Using this representation of a plane, we can define a plane given an n-dimensional vector 0= and offset 00. This vector and offset combination would define the plane 0o +01x1 + 02x2 + -.. + 0nx, = 0. One feature of this representation is that the vector 0 is normal to the plane. 2. (a) 1 point possible (graded) Given a d-dimensional vector 0 and offset 0o which describe a hyperplane p, how many alternative descriptions e' and e are there for p? 0 1
To check if a vector x is orthogonal to a plane p characterized by 0 and 00, we check whether x = ae for some a E R Ox0 0 x0 = 0
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