Which of the following matrix factorizations is primarily used for solving least squares problems and is known for its numerical stability?
Question 2
In the context of LU decomposition, what is the primary purpose of pivoting?
Question 3
Given a matrix $\mathbf{A}$, its Singular Value Decomposition (SVD) is $\mathbf{A} = \mathbf{U}\mathbf{\Sigma}\mathbf{V}^T$. What do the columns of $\mathbf{U}$ represent?
Question 4
Which of the following scenarios would most benefit from using QR decomposition for solving a linear system $\mathbf{Ax} = \mathbf{b}$?
Question 5
Consider a matrix $\mathbf{A}$ that can be decomposed into $\mathbf{A} = \mathbf{LU}$. What is the primary advantage of this decomposition when solving multiple linear systems with the same matrix $\mathbf{A}$ but different right-hand side vectors $\mathbf{b}$?
