Recent content by Boom101

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    Finding Characteristic Polynomial of Matrix B

    Thanks again mark.
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    Finding Characteristic Polynomial of Matrix B

    Thanks again mark.
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    Showing a matrix is diagonalizable and calculating powers

    I did the work again and found my mistake. The eigenvectors are [0 -1 2], [2 -1 1], [-1 0 1]
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    Showing a matrix is diagonalizable and calculating powers

    Homework Statement Consider the matrix A = | 7 16 8| |-1 0 -1| |-2 -10 -3| Show that A is diagonalizable. Find an invertible matrix P and diagonal matrix D and use the obtained result in order to calculate A^2 and A^3 Homework Equations Determinant equation I suppose. D is the diagonal...
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    Finding Characteristic Polynomial of Matrix B

    That was the exact problem statement. It was b) from which a) was the question above. Regarding my first question, I'm left with about 20 different combinations of variables which I can't simplify. If I can't simplify, should I just leave it the way it is?
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    Finding Characteristic Polynomial of Matrix B

    Ok thanks. I just have another question. Let M be an nxn matrix this is invertible and let A be an nxn matrix. show that the eigenvalues of (inverse of M) are the roots of the polynomial p(λ) = det(A-λM). I just have no idea where to go on this one.
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    Finding Characteristic Polynomial of Matrix B

    Homework Statement B = |a 1 -5 | |-2 b -8 | |2 3 c | Find the characteristic polynomial of the following matrix. Homework Equations None The Attempt at a Solution So basically I have to find the det(B-λI). No matter what I do to the matrix I can't make the...
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    Solving f(x)=0: Horizontal Asymptote

    And i did mean 2 / (x+3). I was just copying what was down on the page, but I know my original post was wrong. I was looking for the y intercept, which there isn't, correct? I'm just wondering if on top of finding if the interval increase/decrease and concavity I should also find the behavior...
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    Solving f(x)=0: Horizontal Asymptote

    Is it absolutely necessary to find out the behavior of x -> a if you calculate whether the interval increases/decreases and the concavity?
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    Solving f(x)=0: Horizontal Asymptote

    Homework Statement f(x) = 2 / x + 3Homework Equations NoneThe Attempt at a Solution Nvm I'm an idiot. Y=0 is a horizontal asymptote
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    Solving a Matrix: How to Go Further?

    Thanks everyone for the help. How do I find values other than h = 3?
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    Solving a Matrix: How to Go Further?

    Ok so I get h-2 / 2h-6 I still don't understand how to finish.
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    Matrix Properties : A2 + 6A +9I3 = 0, show that A is invertible

    Thanks Ivy
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    Solving a Matrix: How to Go Further?

    A = | 1 2 0 | | 0 2h-6 h-2 | | 0 1 1 | How do I go further? 2h - 6 = 1? Or should it be (2h-6 times a constant x) = 1, and then write the answer in terms of x? I thought of also using x(2h-6) = 1, isolate x and replace it in x(h-2) = 0 to put the answer in terms of h...
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    Matrix Properties : A2 + 6A +9I3 = 0, show that A is invertible

    Yeah I knew what I did was wrong. In any case, I have no idea how to show that A is invertible.