Q1 (5 points) First read example 4.6.5. from the Damiano and Little text. For an online copy, click here: httpszllq.utoronto.ca/courses/297154/pages/ex4dot-6-5from-damiano-and-little 4 3 3 4 4332 -l 61:31 41/2 :1 into the graph of 53:2 53/2 = l, which is more easily identifiable as an hyperbola. To see this, rename the variables from the textbook "x" and "y". The question: In this example, the authors diagonalize the matrix ( ) to turn the graph of Explain in detail how one can turn 0.332 + 2b53y ay2 2 1 into r532 ty2 ab ba = 1 for some real numbers 7' and t by diagonalizing a matrix 'of the form ( ) . Note that a and b are real strictly positive numbers. The explanation in example 4.6.5 is missing some details. Be sure to fill in the blanks with any theorems that are being used or details that are missing. You do not have to construct the matrix Q or find any eigenvectors. However, you should still find the eigenvalues in terms of a and b. Then explain how you could find matrix Q (without actually finding it), explain how you would use it, and discuss how to get the equation of the hyperbola in the new basis. Hint 1: You are welcome to look up hyperbolas online. However, knowledge beyond the general equation of an hyperbola is not required for this question. Hint 2: The textbook writes a symbol that looks like Q' but is actually Q\