1. All matrices in the following statements are n x n matrices. Mark each statement TRUE or FALSE. If FALSE, justify. (a) A is diagonalizable if A = PDP-1 for some matrix D and some invertible matrix P. (b) A is diagonalizable if and only if A has n eigenvalues, counting with multiplicities. (c) If A is diagonalizable, the A is invertible. (d) If A is diagonalizable, then A has n distinct eigenvalues.

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.