W1 MATH221
1. (1 point) Library/Rochester/setAlgebra34Matrices/determinan
t_3x3a.pg
Given the matrix
A = 2 4 a a 8 − −7 5 1 2 5 a 3 5;
find all values of a that make jAj = 0. Give your answer as a
comma-separated l
...
W1 MATH221
1. (1 point) Library/Rochester/setAlgebra34Matrices/determinan
t_3x3a.pg
Given the matrix
A = 2 4 a a 8 − −7 5 1 2 5 a 3 5;
find all values of a that make jAj = 0. Give your answer as a
comma-separated list.
Values of a: .
Answer(s) submitted:
•
(incorrect)
2. (1 point) Library/Rochester/setAlgebra34Matrices/det_inv_3x
3.pg
Consider the following matrix
24
1 3 2
−2 0 0
0 4 4
35
:
(a) Find its determinant.
(b) Does the matrix have an inverse? [Choose/Yes/No]
Answer(s) submitted:
• •
(incorrect)
3. (1 point) Library/Rochester/setLinearAlgebra6Determinants/u
r_la_6_8.pg
Find k such that the following matrix M is singular.
M = 2 4 12−−+24 k −− −3 1 2 1 5 1 3 5
k =
Answer(s) submitted:
•
(incorrect)
4. (1 point) Library/Rochester/setLinearAlgebra6Determinants/u
r_la_6_14.pg
Find the determinant of the matrix
M =
2664
3 0 0 −1
−1 0 −2 0
0 2 0 2
0 3 −1 0
3775
:
det(M) = .
Answer(s) submitted:
•
(incorrect)
5. (1 point) Library/Rochester/setLinearAlgebra6Determinants/u
r_la_6_15.pg
Find the determinant of the matrix
M =
266664
2 0 0 2 0
−2 0 3 0 0
0 −1 0 0 1
0 0 0 1 2
0 3 1 0 0
377775
:
det(M) = .
Answer(s) submitted:
•
(incorrect)
6. (1 point) Library/TCNJ/TCNJ_PropertiesDeterminants/problem9
.pg
If B =2 4 -2 2 -2 -1 1 -1 1 0 1 3 5
then det(B5) =
Answer(s) submitted:
•
(incorrect)
7. (1 point) Library/TCNJ/TCNJ_PropertiesDeterminants/problem8
.pg
A and B are n×n matrices.
Check the true statements below:
• A. If detA is zero, then two rows or two columns are
the same, or a row or a column is zero.
• B. detAT = (−1)detA.
• C. If two row interchanges are made in sucession, then
the determinant of the new matrix is equal to the determinant of the original matrix.
• D. The determinant of A is the product of the diagonal
entries in A.
Answer(s) submitted:
•
(incorrect)
1
This study source was downloaded by 100000830919685 from CourseHero.com on 06-19-2022 23:29:08 GMT -05:00
https://www.coursehero.com/file/52429117/2019W1-MATH-221-ALLSW72UZ1HVJ02WebWork-09pdf/8. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/u
r_la_11_25.pg
Given that~v1 = −11 and~v2 = 0 1 are eigenvectors of the
matrix
A = − −1 0 3 −4
determine the corresponding eigenvalues.
l1 = .
l2 = .
Answer(s) submitted:
• •
(incorrect)
9. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/u
r_la_11_4.pg
Find the eigenvalues of the matrix
C = 2 4 − −22 5 22 19 16 − −5 5 − −19 16 3 5:
The eigenvalues are .
(Enter your answers as a comma separated list. The list you
enter should have repeated items if there are eigenvalues with
multiplicity greater than one.)
Answer(s) submitted:
•
(incorrect)
10. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/
ur_la_11_18.pg
The matrix
A = 2 4 − −2 0 1 0 0 4 −1 0 −1 3 5
has one real eigenvalue. Find this eigenvalue and a basis of the
eigenspace.
The eigenvalue is .
A basis for the eigenspace is ( 2 4 3 5, 2 4 3 5 ):
Answer(s) submitted:
• •
(incorrect)
11. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/
ur_la_11_8.pg
Find the eigenvalues and eigenvectors of the matrix
24
2 0 0
0 −3 0
−2 −3 0
35
:
From smallest to largest, the eigenvalues are l1 < l2 < l3 where
l1 = has an eigenvector 2 4 3 5,
l2 = has an eigenvector 2 4 3 5,
l3 = has an eigenvector 2 4 3 5.
Note: you may want to use a graphing calculator to estimate the
roots of the polynomial which defines the eigenvalues.
Answer(s) submitted:
• • • • • •
(incorrect)
12. (1 point) Library/TCNJ/TCNJ_Eigenvalues/problem9.pg
Determine if v is an eigenvector of the matrix A.
? 1. A =
2664
1 0 4 -7
2 -1 4 -4
0 0 -1 3
0 0 0 2
3775
, v =
2664
35
-1
-1
3775
? 2. A =
2664
1 0 0 -1
-2 -1 0 -2
5 -1 -2 5
0 0 0 2
3775
, v =
2664
-1
001
3775
? 3. A =
2664
-2 -1 0 7
0 -1 0 -3
-3 -1 1 8
0 0 0 2
3775
, v =
2664
00
-1
0
3775
Answer(s) submitted:
• • •
(incorrect)
2
This study source was downloaded by 100000830919685 from CourseHero.com on 06-19-2022 23:29:08 GMT -05:00
https://www.coursehero.com/file/52429117/2019W1-MATH-221-ALLSW72UZ1HVJ02WebWork-09pdf/13. (1 point) Library/TCNJ/TCNJ_Eigenvalues/problem11.pg
The matrix
A = 2 4 0 5 9 5 − −4 9 5 6 −1 3 5
has eigenvalues −4, 1, and 5. Find its eigenvectors.
The eigenvalue −4 has associated eigenvector
24
35
.
The eigenvalue 1 has associated eigenvector
24
35
.
The eigenvalue 5 has associated eigenvector
24
35
.
Answer(s) submitted:
• • •
(incorrect)
14. (1 point) Library/TCNJ/TCNJ_Eigenvalues/problem11.pg
The matrix
A = 2 4 −2 0 0 6 2 0 4 −2 0 3 5
has eigenvalues −2, 0, and 2. Find its eigenvectors.
The eigenvalue −2 has associated eigenvector
24
35
.
The eigenvalue 0 has associated eigenvector
24
35
.
The eigenvalue 2 has associated eigenvector
24
35
.
Answer(s) submitted:
• • •
(incorrect)
15. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/
ur_la_11_28.pg
Find the three distinct real eigenvalues of the matrix
B = 2 4 −0 0 0 5 1 − −4 4 3 −8 3 5:
The eigenvalues are . (Enter your answers as a
comma separated list.)
Answer(s) submitted:
•
(incorrect)
16. (1 point) Library/Rochester/setLinearAlgebra11Eigenvalues/
ur_la_11_15.pg
The matrix
A = −81 −k6
has two distinct real eigenvalues if and only if k < .
Answer(s) submitted:
•
(incorrect)t
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