There are a total 22 problems. The first 3 problems are CALCULATION problems, and
the rest of 19 problems are MULTIPLE choices. All of the MUTIPLE choices problems
have only SINGLE correct answer. Please CLEARLY write your answers with associated
problem numbers on the answer sheet. There will be NO partial credit given to the MUL-
TIPLE CHOICE problems, anything that is not on the answer sheet will NOT be counted.
Problem 1. Given a matrix
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where a is a real number. Find the rank of A| and give the corresponding range of a.