Consider the following three functions: G(x, y) = 4x - 3y + 21 H(x, y, z) = 13x² + y + 3z I(z) = z Which of the following is true regarding the linearity of the functions? A) none of the functions is linear B) all three functions are linear C) h is linear, but g and i are not linear D) i is linear, but g and h are not linear E) g and i are linear, but h is not linear

Question

Quizplus · Accepted Answer

- Function G(x, y) is not linear because it does not satisfy the properties of linearity, namely homogeneity and additivity.
- Function H(x, y, z) is not linear because it contains non-linear terms involving exponents of x and z.
- Function I(z) is linear because it satisfies the properties of homogeneity and additivity. Specifically, I(ax) = aI(x) for any scalar a and I(x+y) = I(x) + I(y) for any vectors x and y.
Therefore, only functions G and I are linear, while function H is not. The correct choice is E.

Consider the Following Three Functions