We have loked at several general matrix transformations in module 1. answer the questions below about these
familiar matrices, and explain your answers.
a. what efect does the identity transformation have on the unit square? what is the area of the image?
confirm your answer using the determinant.
b. how does a dilation with a scale factor of k change the area of the unit square? calculate the determinant of a
matrix representing a pure dilation of k.
c. does a rotation with no dilation change the area of the unit square? confirm your answer by calculating the
determinant of a pure rotation matrix, and explain it

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )