List of top Statistical Science Questions on Linear Algebra

If an n x n matrix A satisfies the equation \(A^2 - 2A + I = 0\), then:
1. \(A^3 = 3A - 2I, A^4 = 4A - 3I\)
2. \(A^3 = 2A - I, A^4 = 4A - 3I\)
3. \(A^3 = 2A^2 - 3I, A^4 = 3A^2 - 4I\)
4. \(A^3 = 4A - 3I, A^4 = 3A - 2I\)

If \(A = \begin{pmatrix} 1 & 1 1 & 1 \end{pmatrix}\), then the entries of \(A^3\) are:

If \(A = \begin{pmatrix} 4 & -6 -8 & 12 \end{pmatrix}\), then a nontrivial solution of \(A x = 0\) is: