Homework Statement
Find the eigenvalues and the eigenvectors for the given matrix.Homework Equations
\[
A =
\left[ {\begin{array}{ccc}
-1 & 6 & 2 \\
0 & 5 & -6 \\
1 & 0 & -2 \\
\end{array} } \right]
\]The Attempt at a Solution
I solved A-\lambda I = 0 and got eigenvalues of -4 and 3...
Wolfram suggests that the correct answer should be 2/9: http://www.wolframalpha.com/input/?i=int+(sqrt(x%2By)(y-2x)^2)+dy+dx,+x%3D0+to+1,+y%3D0+to+1-x+
However, after evaluating my transformation, I got 1892/315, which Wolfram agreed with...
Find the sum of the series...
Homework Statement
Find the sum: {1}^{2} - {2}^{2} + {3}^{2} - {4}^{2} + ... + [\left(-1\right)^{m-1}]{m^2}
and
Find the sum: x + {2x}^{2} + {3x}^{3} + ... + {nx}^{n}
Homework Equations
n/a
The Attempt at a Solution
For problem 1:
I tried...
Homework Statement
Evaluate \int_0^1 \! \int_0^{1-x} \! \sqrt{x+y} \left(y-2x\right)^{2} \, \, \mathrm{d}y \, \mathrm{d}x. by applying the appropriate transformation.Homework Equations
N/AThe Attempt at a Solution
So far, the best I can come up with is u=1-x, v=x+y, which gives me \int_0^1 \...