Consider the matrix \[ M=\begin{bmatrix}1&2&3\\3&1&3\\4&3&6\end{bmatrix}. \] The determinant of \(M^2+12M\) is ______.

Select all choices that are subspaces of \(\mathbb{R}^3\). Note: \(\mathbb{R}\) denotes the set of real numbers.

Which of the following statements is/are TRUE? Note: R denotes the set of real numbers.

Let \(\mathbb{R}\) be the set of real numbers, let \(U\) be a subspace of \(\mathbb{R}^3\), and let \(M\in\mathbb{R}^{3\times3}\) …

Let \[ \mathbf{u}=\begin{bmatrix}1\\2\\3\\4\\5\end{bmatrix}, \] and let \(\sigma_1,\sigma_2,\sigma_3,\sigma_4,\sigma_5\) be the …

Let \(M = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}\) be a \(2 \times 2\) matrix, where \(…