5. Let T: R R be the transformation given by T(x) = proj, (x) where u...

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5. Let T: R³ R³ be the transformation given by T(x) = proj, (x) where u = 2 (a) (5 pts) Show that T is a linear transformation by demonstrating that T(ax+by) = aT(x) +bT(y) for all x, y R³ and scalars a and b. Note, it will be helpful to use properties of the dot product. (b) (5 pts) Find the matrix representation of T under the standard basis. 5. Let T: R³ R³ be the transformation given by T(x) = proj, (x) where u = 2 (a) (5 pts) Show that T is a linear transformation by demonstrating that T(ax+by) = aT(x) +bT(y) for all x, y R³ and scalars a and b. Note, it will be helpful to use properties of the dot product. (b) (5 pts) Find the matrix representation of T under the standard basis.

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To show that the transformation T is linear need to show that it satisfies two properties additi... View the full answer