AI

Mathematics for Machine Learning Exercise 1 : Basic vector operations Let $$ \mathbf{u} = (1,2,-1)^\top, \quad \mathbf{v} = (0,1,3)^\top. $$ Compute: ⟨u, v⟩ \( \| \mathbf{u} \|_2 \) and \( \| \mathbf{v} \|_2 \) Projection of u onto v. Exercise 2 : Linear system Solve: $$ A = \begin{pmatrix} 2 & -1 & 0 \\ 1 & 1 & 1 \\ 0 & 2 & -1 \end{pmatrix}, \quad \mathbf{b} = \begin{pmatrix} 1 \\ 3 \\ -1 \end{pmatrix}, \quad A\mathbf{x} = \mathbf{b}. $$Exercise 3 : Data interpretation Given points (1,2), (2,3), (3,5), form the design matrix X for ...