Homework Answers
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find...
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find A-? using the formula A-1 adj(A). det(A)
3 2 1 1 2 3 3) Let C- 2 6-1and D 0 5 6 0...
3 2 1 1 2 3 3) Let C- 2 6-1and D 0 5 6 0 09 12 0 a) Find det(C) b) Find det (D) c) Find det (CD) d) Find det(DC)
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0...
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0 2 3 loo-1/ and B 1 2 (1 1 -3 -1 2 2 0 / (1) Compute det A. 3 (2 .-1)-(3.0) = 1.(-2) - (0) = -2 (2) Evaluate : det (+(2(342)*)*") (3) Compute det B.
three seperate questions multiple choice 13 and B= Find A -B. 2 . [4:1 Let A=...
three seperate questions multiple choice
13 and B= Find A -B. 2 . [4:1 Let A= -1 6 2 6 7 177 15 12 1 5 5 30 1 5 3 30 7 17 15 36 Let A and B be 3 x 3 matrices with det(A) = 2 and det(B) = -3. Then find det(-A2B). -6 -12 6 12 [5 2 -2 3 -47 0 4 21 _0 Find the determinant of the matrix, A= 10 0 -2 3...
11 -2 31 Let A = 2 1 k Find the value of k for which...
11 -2 31 Let A = 2 1 k Find the value of k for which det A = -10. Your value of k should be an integer 10 -3 -k] Answer: Check Let [ 2 2 -1] A = -1 -11 ( 2 4 -1] Given that 1 is an eigenvalue of A, find a value of k so that (5.-1,k) is in the eigenspace of A corresponding to the eigenvalue I.
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A. What is its eigenvalue? (b) By solving (A+2/)x 0, show that -2 is an eigenvalue of A. (c) Use the results of parts (a) and (b) to write down all...
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A. What is its eigenvalue? (b) By solving (A+2/)x 0, show that -2 is an eigenvalue of A. (c) Use the results of parts (a) and (b) to write down all eigenvalues of A along with their algebraic and geometric multiplicities. Is A diagonalizable? (Note: This question does not require finding eigenvalues by solving det(A XI) 0)
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A....
T-1 2 5 ſi 0 0] Q2. (19 pts) Let B 0 1 8 and C...
T-1 2 5 ſi 0 0] Q2. (19 pts) Let B 0 1 8 and C = 6 3 0 0 0 1 5 4 1] determinants using the properties of determinants: Compute the following a) det($_35") b) det(3C) c) det(B25) d) det (((3C)B)')
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2...
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2 0 4] -11 | 3 | a. Show that uj = 0 , 12 = -3 , uz = 6 are eigenvectors of M, and 1 1 1 determine the corresponding eigenvalues. b. Using your answer to part (a) what is det(M)? c. Using your answer to part (a), what is the characteristic polynomial of M? d. Using your answer to part (a), is...
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1...
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1 2 3 0 5. Calculate the determinant of D 03 [10 points 0 2 0 7 2 1 1 6. Find the inverse of A 1 3 using the method in section 5.3. 10 points
2. Find a general solution of X' = AX if 3 -1 (1A A1 = 12...
2. Find a general solution of X' = AX if 3 -1 (1A A1 = 12 = 2 1 [ 1] 3 -1 (2) A= 1 Xi = 1; 12 = 13 = 2 1 (3) A = 1 Xi = 0; 12 = 13 = 5 1 (4) A= 5 -4 0 0 2 0 2 5 0 0 0 3 1 0-1 1 1 0 0 2 2 - 1 0 1 0 11 = 1; 12 =...
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find A-? using the formula A-1 adj(A). det(A)
3 2 1 1 2 3 3) Let C- 2 6-1and D 0 5 6 0 09 12 0 a) Find det(C) b) Find det (D) c) Find det (CD) d) Find det(DC)
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0 2 3 loo-1/ and B 1 2 (1 1 -3 -1 2 2 0 / (1) Compute det A. 3 (2 .-1)-(3.0) = 1.(-2) - (0) = -2 (2) Evaluate : det (+(2(342)*)*") (3) Compute det B.
three seperate questions multiple choice
13 and B= Find A -B. 2 . [4:1 Let A= -1 6 2 6 7 177 15 12 1 5 5 30 1 5 3 30 7 17 15 36 Let A and B be 3 x 3 matrices with det(A) = 2 and det(B) = -3. Then find det(-A2B). -6 -12 6 12 [5 2 -2 3 -47 0 4 21 _0 Find the determinant of the matrix, A= 10 0 -2 3...
11 -2 31 Let A = 2 1 k Find the value of k for which det A = -10. Your value of k should be an integer 10 -3 -k] Answer: Check Let [ 2 2 -1] A = -1 -11 ( 2 4 -1] Given that 1 is an eigenvalue of A, find a value of k so that (5.-1,k) is in the eigenspace of A corresponding to the eigenvalue I.
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A. What is its eigenvalue? (b) By solving (A+2/)x 0, show that -2 is an eigenvalue of A. (c) Use the results of parts (a) and (b) to write down all eigenvalues of A along with their algebraic and geometric multiplicities. Is A diagonalizable? (Note: This question does not require finding eigenvalues by solving det(A XI) 0)
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A....
T-1 2 5 ſi 0 0] Q2. (19 pts) Let B 0 1 8 and C = 6 3 0 0 0 1 5 4 1] determinants using the properties of determinants: Compute the following a) det($_35") b) det(3C) c) det(B25) d) det (((3C)B)')
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2 0 4] -11 | 3 | a. Show that uj = 0 , 12 = -3 , uz = 6 are eigenvectors of M, and 1 1 1 determine the corresponding eigenvalues. b. Using your answer to part (a) what is det(M)? c. Using your answer to part (a), what is the characteristic polynomial of M? d. Using your answer to part (a), is...
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1 2 3 0 5. Calculate the determinant of D 03 [10 points 0 2 0 7 2 1 1 6. Find the inverse of A 1 3 using the method in section 5.3. 10 points
2. Find a general solution of X' = AX if 3 -1 (1A A1 = 12 = 2 1 [ 1] 3 -1 (2) A= 1 Xi = 1; 12 = 13 = 2 1 (3) A = 1 Xi = 0; 12 = 13 = 5 1 (4) A= 5 -4 0 0 2 0 2 5 0 0 0 3 1 0-1 1 1 0 0 2 2 - 1 0 1 0 11 = 1; 12 =...
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