Linear Algebra Answers

Let x, y and z be three vectors in a vector space V

a. Give a definition of span{x,y, z} in set notation.

Use zero through third order taylor series expansion to predict value of 𝑓(2) using base point as

x = 1 for 𝑓(𝑥) = 7𝑥3 − 3𝑥2 + 5𝑥 − 2

A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic of gravel. Each cubic meter of river sand costs P100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.

A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make P200, 000 profit per hectare planted to rice and P250, 000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant?

Given the augmented matrix below, determine the values of 𝑥 and 𝑦 such that the system is inconsistent or consistent. [4 marks] ( 1 1 3 2 1 2 4 3 1 2 4 3 1 3 𝑥 𝑦 )