Linear Algebra writing proof. Use terms vector equation, linear combination, consistent, inconsistent, parametric solutions, etc.

A brokerage firm offers three mutual funds A, B, C which each bundle shares Google, Tesla, Apple, and Facebook stock. The table below shows how many shares of each stock are bundled into each mutual fund share.

Fund A Fund B Fund C

	Fund A	Fund B	Fund C
Google	4	5	2
Tesla	3	5	4
Apple	3	3	0
Facebook	2	3	2

A. If you buy 10 shares of fund A, 5 shares of B and 8 of fund C, how many total shares of each of the four companies will you own?

b. You wish to obtain 143 shares of Google, 151 shares of Tesla, 81 shares of Apple, and 89 shares of Facebook. Can you accomplish this through purchases of the mutual funds A,B, C?

c. The brokerage firm will charge you a fee of $1 per share of each mutual fund. What is the most economical way for you to obtain your desired totals of 143, 151, 81, 89?

d. Your goal is to own 143 Google, 151 Tesla, 81 Apple, 90 Facebook shares, Can you accomplish this through purchases of the mutual funds A, B, C?