W1 MATH221

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