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Question: Let J be the n X n matrix of all 1's, and consider A = (a - b) I + bJ ; that is,
Confirm that det A = (a - b)n-1 [a + (n - 1)b] as follows:
a. Subtract row 2 from row 1, row 3 from row 2, and so on, and explain why this does not change the determinant of the matrix.
b. With the resulting matrix from part (a), add column 1 to column 2, then add this new column 2 to column 3, and so on, and explain why this does not change the determinant.
c. Find the determinant of the resulting matrix from (b).
Russ, Don, Pamela, and Stephanie are the first names of four friends who all received sports scholarships. Krieger actually has a full ride, because he is a star in two different sports. Use the clues to determine each person's full name.
If you move the equivalent of 1/2 unit horizontally in the direction of the vector (4,-3) estimate the height at your new location on the surface.
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.
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closed box with a square base has to have a volume of 3000 cubic inches. Find a function for the surface area of the box.
Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 50% like country music, 30% like gospel music, and 15% like both.
Find the value of x such that the volume is a maximum.
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