Suppose the m × n matrix A has the form A = A1 A2 Where A1 is a non-singular matrix of dimension n × n and A2 is an arbitrary matrix of size (m − n) × n. Show that the 2-norm of the pseudo-inverse matrix is less than the 2-norm of the inverse of A1.

Agroup of student volunteers participates in a study designed to assess several behavioral interventions for improving output in a repetitive task. prior to the beginning of the study, all volunteers unknowingly observed, and their output is measured. at the beginning of the study, prior to any intervention, the volunteers perform the same task under the observation of a study administrator, and their overall output increases. which of the following terms describes this phenomenon? a. simpson's paradox b. hawthorne effect are d. novelty effect d. pygmalion effect e. observer-expectancy effect