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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2017 • Question 1

Question

Math 6510 • Differentiable Manifolds Summer 2017 • Question 1

Let \(A:\mathbb {R}^2\to \mathbb {R}^3\) be given by \[ A= \begin {pmatrix} 3 & 2\\ 1 & 4\\ 0 & -1 \end {pmatrix} \] Find \(\lambda \) such that \(A^*(3dy_1\wedge dy_2-2dy_2\wedge dy_3+7dy_1\wedge dy_3) =\lambda dx_1\wedge dx_2\).

Raw LaTeX

Let \(A:\R^2\to\R^3\) be given by
\[
  A=
  \begin{pmatrix}
    3 & 2\\
    1 & 4\\
    0 & -1
  \end{pmatrix}
\]
Find \(\lambda\) such that
\(A^*(3dy_1\wedge dy_2-2dy_2\wedge dy_3+7dy_1\wedge dy_3)
=\lambda dx_1\wedge dx_2\).

Topic Tags

Differential Forms and Exterior Calculus