21-241 Matrix Algebra
Homework #1:
Exercises: Due Thursday, May 20
Section 1.1: 2, 8, 14, 15, 20, 25, 33, 34
Section 1.2: 3, 7, 12, 14, 16, 23, 29, 31
Section 1.3: 3, 7, 10, 12, 13, 17, 22
Homework #2:
Exercises: Due Tuesday, May 25
Section 1.4: 10, 12, 15, 19, 35
Section 1.5: 2, 6, 16, 29-32, 35
Section 1.6: 4, 6, 12
Homework #3:
Exercises: Due Wednesday, May 26
Section 1.7: 3, 6, 12, 20, 23, 28, 31, 33
Section 1.8: 4, 10, 12, 15, 17, 18, 25, 31
Section 1.9: 3, 6, 7, 9, 13, 17, 25, 29-31
Homework #4:
Exercises: Due Tuesday, June 1
Section 2.1: 9, 10, 13, 14, 23, 24, 27, 28
Section 2.2: 2, 7, 13-16, 20, 31, 33
Homework #5:
Exercises: Due Thursday, June 3
Section 2.3: 7, 14, 18, 19, 22, 28, 33
Section 2.7: 2, 5, 7, 14, 17, 18
Problem A: Refer to the triangle in Exercise 2.7.2. Suppose you wish
to rotate this triangle 60 degrees with respect to the point (6,8).
Draw a sketch which shows the initial position of the triangle, and illustrates approximately where the triangle would
end up after this transformation. (You do not need to try and guess the
coordinates of the new vertices -- just illustrate their approximate
positions.) Then use the matrix you found in Exercise 2.7.7 to perform
this rotation. This will give you the new vertices. Finally,
draw another sketch which illustrates the transformation.
Homework #6:
Exercises: Due Tuesday, June 8
Section 2.8: 3, 6, 11-15, 24, 26, 27
Section 2.9: 1, 5, 12, 14, 16, 20
Section 3.1: 7, 11, 23, 37, 38
Homework #7:
Exercises: Due Thursday, June 10
Section 3.2: 1, 8, 13, 23, 26, 31, 34-36
Section 5.1: 6, 10, 16-20, 27, 29, 30, 33
Section 5.2: 1, 8, 10, 17, 18, 20
Homework #8:
Exercises: Due Tuesday, June 15
Section 5.3: 1, 3, 15, 18, 24, 27, 31
Section 5.5: 5
Problem A: Find all real and complex eigenvalues of the 3 X 3
matrix A below, and for each eigenvalue, find a corresponding
eigenvector.
[1 1 -1]
A = [0 1 0]
[1 0 1]
Problem B: Find all real and complex roots of the polynomial
x^3 + x^2 + 17x - 87
Hints: First look for real integer roots by substituting values
such as 0, 1, -1, 2, -2, etc., into the polynomial, in hopes that you
will find a
"nice" root r. If you find one, then you know that the polynomial can
be factored as follows:
(x - r) (x^2 + ax + b)
By multiplying these factors, you can determine the appropriate values
for
a and b. Finally, you can find the roots of the quadratic factor,
using the
quadratic formula if necessary.
Problem C: Find all real and complex eigenvalues of the 4 X 4
matrix A below, and for each eigenvalue, find a corresponding
eigenvector.
[1 -1 1 -1]
A = [1 1 1 1]
[0 0 1 1]
[0 0 1 1]
Section 5.6: 3, 10, 12, 14, 15, 17ab
Homework #9:
Exercises: Due Thursday, June 17
Section 6.1: 2, 3, 6, 8, 9, 11, 14-18, 28
Section 6.2: 2, 3, 7, 10, 12, 13, 17, 20, 22, 25, 28
Homework #10:
Exercises: Due Monday, June 21
Section 6.3: 1, 5, 9, 12, 13, 16, 17
Section 6.4: 3, 7, 11, 12
Homework #11:
Exercises: Due Wednesday, June 23
Section 6.5: 2, 5, 11, 19, 20, 22, 25
Section 6.6: 2 (include a sketch of the data points and the
least-squares
line), 7 (designated with [M] but not bad; include a sketch of the data
points and the least-squares parabola approximating
the data. You may use technology to determine what this graph looks
like,
or use algebraic methods, such as completing the square, to determine
the
location of the parabola's vertex.)
Section 7.1: 1-12, 16, 18, 21, 24, 27-30
Homework #12:
Exercises: Due Friday, June 25
Section 7.2: 1, 5, 8, 12, 19
Section 7.3: 5, 8, 10, 11
Section 7.4: 1-4, 11, 13, 15-17