List of top Data Science and Artificial Intelligence Questions on Matrix

Consider the 3 × 3 matrix M = \(\begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix}.\)
The determinant of (M² + 12M) is ________.

Let \(u=\begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix}\), and let σ₁, σ₂, σ₃, σ₄, σ₅ be the singular values of the matrix M= uu^T (where u^T is the transpose of u).The value of \(Σ^{5}_{i=1}σ_i\) is

For any binary classification dataset, let \(S_B\in \R^{d\times d}\) and \(S_W\in \R^{d\times d}\) be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by \(u^* \in \R ^d\), that maximizes
\(J(u)=\frac{u^TS_Bu}{u^TS_Wu}\)
If λ = J(u*), S_W is non-singular and S_B ≠ 0, then (u*, λ) must satisfy which ONE of the following equations ?
Note : R denotes the set of real numbers.

Consider the matrix \(M=\begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix}\).
Which ONE of the following statements is TRUE ?