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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1994 • Question 11

Question

Math 6310 • Algebra Fall 1994 • Question 11

Show that the elements \(e_1\wedge e_2+e_3\wedge e_4\), \(e_1\wedge e_3+e_3\wedge e_4\), and \(e_5\wedge e_6+e_1\wedge e_3\) are linearly independent in \(\Lambda ^2\mathbb {R}^6\), where \(\{e_1,e_2,e_3,e_4,e_5,e_6\}\) is a basis for \(\mathbb {R}^6\).

Raw LaTeX

Show that the elements
\(e_1\wedge e_2+e_3\wedge e_4\), \(e_1\wedge e_3+e_3\wedge e_4\), and
\(e_5\wedge e_6+e_1\wedge e_3\) are linearly independent in
\(\Lambda^2\mathbb{R}^6\), where \(\{e_1,e_2,e_3,e_4,e_5,e_6\}\) is a basis for
\(\mathbb{R}^6\).

Topic Tags

Ideals in Quadratic Integer Rings and Exterior Powers