Math 215 HW #10 Solutions
1. Problem 5.2.14. Suppose the eigenvector matrix S has S T = S 1 . Show that A = S S 1 is
symmetric and has orthogonal eigenvectors.
the eigenvectors of A. Then, since S T =
Math 215 HW #1 Solutions
1. Problem 1.2.3. Describe the intersection of the three planes u + v + w + z = 6 and u + w + z = 4
and u + w = 2 (all in four-dimensional space). Is it a line or a point or a
Math 215 HW #7 Solutions
1. Problem 3.3.8. If P is the projection matrix onto a k -dimensional subspace S of the whole
space Rn , what is the column space of P and what is its rank?
Answer: The column
Math 215 HW #8
Due 5:00 PM Thursday, April 1
Reading: Sections 4.14.3 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detailed i
Math 215 HW #9
Due 5:00 PM Thursday, April 8
Reading: Sections 4.4, 5.15.2 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detai
Math 215 HW #9 Solutions
1. Problem 4.4.12. If A is a 5 by 5 matrix with all |aij | 1, then det A
big formula or pivots should give some upper bound on the determinant.
. Volumes or the
Answer: Let v
Math 215 HW #10
Due 5:00 PM Thursday, April 15
Reading: Sections 5.25.4 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detailed
Math 215 HW #11
Due 5:00 PM Thursday, April 29
Reading: Sections 5.55.6 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detailed
Math 215 HW #11 Solutions
1. Problem 5.5.6. Find the lengths and the inner product of
x=
2 4i
4i
and y
2 + 4i
.
4i
Answer: First,
x
2
= xH x = [2 + 4i 4i]
2 4i
= (4 + 16) + 16 = 36,
4i
so x = 6. Likew
Math 215 HW #7
Due 5:00 PM Thursday, March 25
Reading: Sections 3.33.4 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detailed
Math 215 HW #6 Solutions
1. Problem 3.1.14. Show that x y is orthogonal to x + y if and only if x = y .
Proof. First, suppose x y is orthogonal to x + y. Then
0 = x y, x + y
= (x y)T (x + y)
= xT x +
Math 215 HW #2
Due 5:00 PM Thursday, February 4
Reading: Sections 1.41.5 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detaile
Math 215 HW #2 Solutions
1. Problem 1.4.6. Write down the 2 by 2 matrices A and B that have entries aij = i + j and
bij = (1)i+j . Multiply them to nd AB and BA.
Solution: Since aij indicates the entr
Math 215 HW #3
Due 5:00 PM Thursday, February 11
Reading: Sections 1.61.7 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detail
Math 215 HW #4
Due 5:00 PM Thursday, February 18
Reading: Sections 2.12.2 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detail
Math 215 HW #4 Solutions
1. Problem 2.1.6. Let P be the plane in 3-space with equation x + 2y + z = 6. What is the
equation of the plane P0 through the origin parallel to P? Are P and P0 subspaces of
Math 215 HW #5
Due 5:00 PM Thursday, February 25
Reading: Sections 2.32.4, 2.6 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration d
Math 215 HW #4 Solutions
1. Problem 2.3.6. Choose three independent columns of U . Then make two other choice. Do the same for A. You have found bases for which spaces? 2341 2341 0 6 7 0 0 6 7 0 U = 0
Math 215 HW #6
Due 5:00 PM Thursday, March 18
Reading: Sections 3.13.2 from Strangs Linear Algebra and its Applications, 4th edition.
Problems: Please follow the guidelines for collaboration detailed
Math 215 HW #1
Due 5:00 PM Thursday, January 28
Reading: Sections 1.11.3 from Strangs Linear Algebra and its Applications, 4th edition. Reading
and understanding the material from the textbook is an i