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Math H54 Honors Linear Algebra Quiz #1
Problem 1
Consider the vector (5, 3), expressed in the standard basis (i.e. {(1, 0),(0, 1)}). What are its coordinates with respect to the basis defined by B = {(1, 1),(1, −1)}?
Problem 2 Recall that a function f : R → R is linear if f(cx) = cf(x), and f(x + y) = f(x) + f(y). Are the following functions linear:
a) f(x) = 2x,
b) f(x) = x 2 ,
c) f(x) = x + 2?
Problem 3 Let ABC be a triangle. Is it true that there exists only one point M, such that MA + MB + MC = 0? What if we change the condition to 2MA + MB + MC = 0?