Written Homework 9 – Zack wants to buy fish and plants

  

Written Homework 9, Due April 25
Written homework is to be handwritten and handed in at the beginning of discussion. In extenuating circumstances you can notify your Teaching Assistant via email before discussion, and homework can be submitted via alternative means the same day of discussion, under agreement with your Teaching Assistant. Otherwise the homework will be considered late. Show all your work, correct answers without supporting work will not receive full credit.
Question 1 (3 points) Zack wants to buy fish and plants for his aquarium. Each fish costs $2.30, each plant costs $1.70. He buys a total of 11 items and spends a total of $21.70. Set up a system of linear equations that will allow you to determine how many fish and how many plants Zack bought, and solve the system.
Question 2 (4 points) Determine all c such that the following system has (a) (2pts) infinitely solutions and (b) (2pts) no solutions.
2x− 3y = 5 4x− 6y = c
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Written Homework 9, Due April 25
Question 3 ( 8 points) Find the augmented matrices and reduce the following systems of linear equa- tions to upper triangular form and solve. Show and explain your row operations.
(a) (2 points)
5x+ 2y = 12
−x+ 3y = 1
(b) (2 points)
7x− y = 4 3x+ 3y = 1
(c) (2 points)
3x− y = 1 −3x+ y = 4
(d) (2 points)
2x− 3y + z = −1 x+ y − 2z = −3 3x− 2y + z = 2
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Written Homework 9, Due April 25
Question 4 (6 points) Consider the matrices:
A =
??√3 1 0−1 √3 0 0 0 −5
?? , B = ??x −14 01
4 y 0 0 0 z
?? (a) (3 points) Solve for x, y, and z such that
AB =
??1 0 00 1 0 0 0 1
??
(b) (2 points) Evaluate BA using the values for x, y, and z found in (a).
(c) (1 point) What can you say about the matrix B?
Question 5 (4 points) Suppose A is a 3 × 4 matrix, B is an m × n matrix, and x =
??xy z
??. For what values of m and n are the following products defined? (a) A ·B
(b) B ·A
(c) B · x
(d) x ·B
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Written Homework 9, Due April 25
Question 6 (4 points) (Review Problem) Find a MacLaurin series which represents
∫ xe−x
3 dx. Don’t
forget “+C”. Hint: Start with the MacLaurin series for ex.
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