An ML specialist is fitting a linear least squares regression model on 1,000 examples and 50 features, and notices two features are perfectly linearly dependent. Why is this problematic for linear least squares regression?

Perfect linear dependence between features means one feature can be expressed as a linear combination of another. In linear least squares regression, this leads to a design matrix (X) that is not full rank. When calculating the coefficients (beta) using the normal equation (beta = (X^T X)^-1 X^T y), the matrix (X^T X) becomes singular, meaning its determinant is zero and it does not have an inverse. This prevents a unique solution for the regression coefficients. Backpropagation is used with gradient descent, not directly with the normal equation for linear least squares. The form of the loss function (mean squared error) does not change due to feature dependence, though optimization might struggle. Linear dependence does not introduce nonlinearity; it's a specific issue within linear relationships.