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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2024 • Question 2

Question

Math 6310 • Algebra Fall 2024 • Question 2

Let \(V:=\mathbb {Z}^3\) and \(L\) the submodule of \(V\) spanned by the columns of the matrix \[ A:=\begin {bmatrix} 4&2&2\\ 2&2&6\\ 2&4&4 \end {bmatrix} \]

Find invertible matrices \(Q\) and \(P\) such that the matrix \(QAP\) is diagonal.

Raw LaTeX

Let \(V:=\mathbb{Z}^3\) and \(L\) the submodule of \(V\) spanned by the columns of the matrix
\[
A:=\begin{bmatrix}
4&2&2\\
2&2&6\\
2&4&4
\end{bmatrix}
\]

Find invertible matrices \(Q\) and \(P\) such that the matrix \(QAP\) is diagonal.

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization