Recent content by annpaulveal

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    Pigeonhole Principle and Boolean Matrices

    Would a better solution be to say that the sum of 51 in a 64-square Boolean matrix implies there are are 13 0s to be placed, and they can't be placed in such a way that each row/column combination adds up to 13 or less?
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    Pigeonhole Principle and Boolean Matrices

    Homework Statement Let A be an 8x8 Boolean matrix. If the sum of A = 51, prove there is a row and a column such that when the total of the entries in the row and column are added, their sum is greater than 13. The Attempt at a Solution I considered a selection of one row and one column...
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    Combinations/Permutations of Seating at a Circular Table

    No, arrangements that are rotations of another are considered alike and should not be counted twice.
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    Combinations/Permutations of Seating at a Circular Table

    Okay, so you're saying I should start with a 12-person table, where the men and women can both be arranged in 5! ways, and then multiply this by 36 choose 3 for the three remaining women, and finally divide this by 15? So, [(5!)(5!)(36 choose 3)] / 15?
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    Combinations/Permutations of Seating at a Circular Table

    Homework Statement In how many ways can a group of 9 women and 6 men be seated at a circular table if no two men can be seated next to each other? Homework Equations The Attempt at a Solution I have come up with a solution, but I'm unsure if my reasoning is correct...
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    Using Matrix Multiplication to Obtain Another Matrix

    I haven't been taught how to use determinants like you said, and it wouldn't be possible for a to be an imaginary number for this solution. If I wasn't clear, I have to figure out some kind of combination of multiplying matrixes A-D in order to get E as the result. First, I have to figure out...
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    Using Matrix Multiplication to Obtain Another Matrix

    Sorry, I still haven't been able to make any progress at all. Thanks anyway.
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    Using Matrix Multiplication to Obtain Another Matrix

    Thanks for your help, but I'm still struggling tremendously. I understand that a will most likely be 0 or -1 (or maybe 1, but that would make C and D the same identity matrix). Is there any other guidance I could get?
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    Using Matrix Multiplication to Obtain Another Matrix

    Homework Statement I need to use matrix multiplication of matrices A-D to obtain matrix E. I also need to set a equal to some value that would allow me to perform this multiplication. Homework Equations The matrixes I need to multiply: A = [1, 1; 0, 1] B = [1, 0; 1, 1] C = [a, 0...
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    Find all unit vectors orthogonal to the line

    Homework Statement Find all the unit vectors orthogonal on the line L. Homework Equations L passes through the vectors u = [9; 7] and v = [1; -5] The Attempt at a Solution I found the slope of L from the two vectors: 3/2. I know that to be orthogonal, the vector will have a...
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    Reduce the boolean expression to two literals

    Never mind, just solved it! Last steps: BD (A(C+C') + A') BD (A+A') BD
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    Reduce the boolean expression to two literals

    I fixed the errors, sorry. Can someone tell me where to go next?
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    Reduce the boolean expression to two literals

    Homework Statement ABC'D + A'BD + ABCD The Attempt at a Solution Here is as far as I have gotten: BD (AC' + A' + AC) BD (AC' + A') According to Wolfram Alpha, the answer should just be BD. Can someone help me get there?
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    Finding the area of one loop of the lemniscate

    I'm sorry, I really don't understand. How can I integrate wrt r without setting the limits of my integrand first? What would those limits be?
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    Finding the area of one loop of the lemniscate

    Homework Statement Find the area of the region bounded by one loop of the lemniscate r2 = a2sin(2θ) with a > 0 using double integration. Homework Equations The Attempt at a Solution I was able to figure out the limits of integration for theta (0 to ∏/2), but what would my...