MA212: Assignment # 2
Required Reading:
• Read Sections 8.4-8.6 and 8.8.
To be turned in March 22nd at the start of class.
1. Textbook § 8.4 #’s 14, 18, 28 (Be smart about minimizing work in problem 28.)
2. Textbook §8.5 #’s 9, 13, 23, 24, 38, 40 (# 40 is not asking you to do any operations or refer to any specific matrix.
It’s just asking you to do a simple algebra calculation or two.)
3. Textbook §8.6 #’s 1, 7, 17, 22. (Note, for problem 7, do not follow the text book’s instructions. Never use the
adjoint formula. Use row operations to produce the inverse. )
4. Textbook §8.8 #’s 2, 5, 12, 16, 21.
5. Application: The Vandermonde matrix is used in applications of statistics and data analysis. It has the form


1 x1 x21 . . . xn−1
1
 1 x2 x22 . . . xn−1 
2


 .
.. 
 ..
. 
1
xn
x2n
...
xn−1
n
Compute the determinants of a 2 × 2 and 3 × 3 Vandermonde matrix. With the 3 × 3 case, use the skills you’ve seen
demonstrated in class to wisely reduce the amount of work. Using cofactor expansion is a bad idea. Instead, use
row operations to get a triangular matrix. Start computing the 4 × 4 case. Once you see the pattern, state what
you think the n × n determinant would be. You don’t need to prove your answer rigorously, just explain the idea.
6. The Vandermonde matrix in the last problem can be applied to finding a polynomial that fits data you’ve collected.
Suppose your experiment collects the following three points to data: (1, −1), (2, 3), and (4, −2). We want to find a
second degree polynomial which fits this data, f (x) = a + bx + cx2 . In our problem x1 = 1, x2 = 2, and x3 = 4. Use
the given data, and the Vandermonde matrix (you won’t need its determinant), to find a, b, and c.
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