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Question 1: Find a basis for the orthogonal complement of
Question 2: Find a vector that is orthogonal to both
Question 3: What is the dimension of the orthogonal complement of span
Question 4: Let W = span
(a) Find an orthonormal basis for W.
(b) What is the orthogonal projection of onto W.
(c) Write as the sum of a vector in W and a vector in W⊥.
(d) Find the projection matrix P corresponding to orthogonal projection onto W.
Question 5: If A and B are 3 × 3 matrices with det(A) = 4 and det(B) = 1. What is the determinant of C = 2AT A-1BA?
Question 6: Let A be a n × n matrix with AT = A-1. What can you say about det(A)?
Question 7: Use Cramer's rule to solve the system:
x1 + x2 + x3 = 4
x1 - x2 - x3 = 0
x1 + 2x2 + 3x3 = 9
A rancher has 1200m of fencing to enclose 2 rectangular corrals. The corrals have the same dimensions and one side in common. What dimensions will maximize the enclosed area?
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1 consider the data set given in the accompanying table. complete parts a through
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the elevation of Death Valley, California. If Death Valley is 282 ft below sea level, find the elevation of Mount Whitney.
Mortgages and Taxes Assignment (Total 40 Points) Question 1: (20 Points) a) You are purchasing a business building valued at $225,000. You can find a mortgage at 5% if you can put 20% down. You believe your business can support a $1,000 a month mortg..
Suppose you are going to flip a coin once. What is the set of possible outcomes for this? Suppose you are going to flip a coin twice. What is the set of possible outcomes for this?
Discussion question 1:Can we apply transshipment models to inventory applications? Why or why not? Is the transportation model an example of decision making under certainty or decision making under uncertainty? Why?
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