State whether the following statements are true or false, with reasoning:

a. Let V := R 2 . Let + denote the usual (vector) addition on R 2 . Define a scalar multiplication ∗ by assigning α ∗ (x, y) = (αy, αx), for any α ∈ R and (x, y) ∈ R 2 . Then (V, ∗, +) is not a vector space.
b. Now let V = R 2×2 , the set of all 2 × 2 real matrices. Let + denote the usual matrix addition (as mentioned in class). But define a scalar multiplication
c. by assigning α • A = O, for any α ∈ R, and O is the zero matrix in R 2×2 . Then, (V, •, +) is a vector space.

What’s 8y+48 and factor each expression completely

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3

Use a calculator to verify that σ(x) = 62, σ(x2) = 1034, σ(y) = 644, σ(y2) = 93,438, and σ(x y) = 9,622. compute r. (enter a number. round your answer to three decimal places.) as x increases from 3 to 22 months, does the value of r imply that y should tend to increase or decrease? explain your answer. given our value of r, y should tend to increase as x increases. given our value of r, we can not draw any conclusions for the behavior of y as x increases. given our value of r, y should tend to remain constant as x increases. given our value of r, y should tend to decrease as x increases.