Let TA : R" → R" be multiplication by an invertible matrix A. Suppose that B = for R". {b1, b2, ... , b,} is a basis Prove that T(B) = {T(b1), T(b2), ... ,T(b,)} is also a basis for R".

Show your work please.

Determine whether ? = [−9, −4,1] can be written as a linear combination of  ? = [−1, −2,1] and ? = [3, −1,1]. Provide a full algebraic solution.

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). x 3 6 12 20 26 y 60 95 140 160 189 (a) Make a scatter diagram of the data and visualize the line you think best fits the data.   Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website.   (b) Would you say the correlation is low, moderate, or strong?  low moderate     strong Would you say the correlation is positive or negative?  positive negative     (c) Use a calculator to verify that          x = 67,           x2 = 1265,           y = 644,           y2 = 93,546,  and          xy = 10,544.  Compute r. (Round your answer to three decimal places.)  As x increases from 3 to 26 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…