1
1
111.5
1
2
97.7
1
3
126.1
2
1
94.4
2
2
70.5
2
3
93.1
3
1
73.9
3
2
56.2
3
3
84.6
In many agricultural and biological experiments, one may use a
two‑way model with only one observation per cell. When one of the
factors is related to the grouping of experimental units into more
uniform groups, the design may be called a randomized complete
block design (RCBD). The analysis is similar to a two‑way...
2. Given A = | 2 1 0 1 2 0 1 1 1 |.
(a) Compute eigenvalues of A.
(b) Find a basis for the eigenspace of A corresponding to each
of the eigenvalues found in part (a).
(c) Compute algebraic multiplicity and geometric multiplicity of
each eigenvalue found in part (a).
(d) Is the matrix A diagonalizable? Justify your answer
Question2.
Let A = [2 1 1
1 2 1
1 1 2 ].
(a) Find the characteristic polynomial PA(λ) of A and the
eigenvalues of A. For convenience, as usual, enumerate the
eigenvalues in decreasing order λ1 ≥ λ2 ≥ λ3.
(b) For each eigenvalue λ of A find a basis of the corresponding
eigenspace V (λ). Determine (with a motivation) whether V (λ) is a
line or a plane through the origin. If some of the spaces V...
Let A = 2 1 1
1 2 1
1 1 2
(a) Find the characteristic polynomial PA(λ) of A and the
eigenvalues of A. For convenience, as usual, enumerate the
eigenvalues in decreasing order λ1 ≥ λ2 ≥ λ3.
(b) For each eigenvalue λ of A find a basis of the corresponding
eigenspace V (λ). Determine (with a motivation) whether V (λ) is a
line or a plane through the origin. If some of the spaces V (λ) is...
2.69 a, c
2
1
1
1
1
3
2
6
1
1
2
1
1
3
2
1
1
2
1
3
4
3
2
5
4
2
2
2
1
1
Refer to the data set above, with 30 values.
Find the range, variance, and standard deviation of this data
set.
Eliminate the smallest and largest value from the data set and
repeat part a. What effect does dropping both of these measurements
have on the measures of...