Let W be a subspace of R", and let W+ be the set of all vectors orthogonal to W. Show that W+ is a subspace of R" using the following steps. a. Take z in W", and let u represent any element of W. Then z•u=0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in W+.) b. Take z, and z, in w*, and let u be any element of W. Show that z, +z, is orthogonal to u. What can you conclude about z, + zz? Why? c. Finish the proof that W+ is a subspace of R". ..... a. How can two vectors be shown to be orthogonal? O A. Determine if the dot product of the two vectors is greater than zero. B. Determine if the dot product of the two vectors is less than zero. C. Determine if the dot product of the two vectors is zero.

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