Gif a is a real n×n matrix, then we have seen that < v, w > a: = v t ∗a∗ w defines a bilinear pairing on r n which is symmetric iff a is a symmetric matrix. if a is symmetric, we call a positive definite iff < v, v > a > 0 for all 0 6= v ∈ r n (in other words, < −,− > a is an inner product on r n). a) [1 pt] suppose b is the matrix given by b = 1 1 1 2 and x = [x1 x2] t ∈ r 2 . find an expression for x t ∗ b ∗ x in terms of x1 and x2. b) [1 pt] using your work in part a), show that the matrix b above is positive definite.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

idk

step-by-step explanation:

answer: the center is the median and/or mean of the data. the spread is the range of the data. and, the shape describes the type of graph. the four ways to describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform. good luck

step-by-step explanation: