System of Equations Practice Exam Questions and Answers

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 1/24 wait=867015, due=1701583140, due2=0 Question number 1. Your answer was B. Correct. Solve the system of equations. A B C D E F None of the above.

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 2/24 Question number 2. Your answer was B. Wrong. Give the solution set to the system of equations A B C D E F None of the above. Question number 3.

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 3/24 You did not answer this question. Wrong. Which of the following gives the correct matrix for this system of equations in reduced row echelon form? A B

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 4/24 C D E F None of the above. Question number 4. You did not answer this question. Wrong. For what values of a does the system below have nontrivial solutions?

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 5/24 A -12 B -4 C 12 D -3 E 3 F None of the above. Question number 5. Your answer was D. Correct. Given: Compute AC - BD .

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 6/24 A B C D E F None of the above. Question number 6.

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 7/24 You did not answer this question. Wrong. The matrices A and B are given by and D = AB. Give the value of d 3,1 . A 10 B -6 C 9 D -3 E 8 F None of the above. Question number 7. You did not answer this question. Wrong.

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 8/24 The matrices A, B and C are given by and D = AB - 4C. Give the value of d 2,3 . A -16 B -13 C -12 D 3 E -10 F None of the above. Question number 8. You did not answer this question. Wrong. Let

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e6824733f… 9/24 Find A -1 , if it exists. A B C D

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 10/24 E F None of the above. Question number 9. You did not answer this question. Wrong. Use Cramer's rule to give the value of y for the solution set to the system of equations A B C D

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 11/24 E F None of the above. Question number 10. You did not answer this question. Wrong. Determine the values of λ for which the system below has nontrivial solutions. A B C D E

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 12/24 F None of the above. Question number 11. You did not answer this question. Wrong. Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) A Eigenvalues: 4, -2, 3; Number of independent eigenvectors: 3 B Eigenvalues: 4, 4, 3; Number of independent eigenvectors: 2 C Eigenvalues: 4, 2, -3; Number of independent eigenvectors: 3 D Eigenvalues: 4, 2, 3; Number of independent eigenvectors: 3 E Eigenvalues: 4, 2, 2; Number of independent eigenvectors: 2 F None of the above.

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 13/24 Question number 12. You did not answer this question. Wrong. Find the eigenvalues and number of independent eigenvectors. (Hint: -2 is an eigenvalue.) A Eigenvalues: -2, 1, -1; Number of independent eigenvectors: 3 B Eigenvalues: -2, 1, 1; Number of independent eigenvectors: 3 C Eigenvalues: 2, 2, 1; Number of independent eigenvectors: 2 D Eigenvalues: -2, -2, 1; Number of independent eigenvectors: 2 E Eigenvalues: -2, 2, 1; Number of independent eigenvectors: 3 F None of the above. Question number 13.

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 14/24 You did not answer this question. Wrong. Given the linear differential system x ' = A x with Determine if u , v form a fundamental solution set. If so, give the general solution to the system. A B C D

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 15/24 E F None of the above. Question number 14. You did not answer this question. Wrong. Find the general solution to the system x ' = A x where A is the given matrix. A x ( t )= B x ( t )= C x ( t )=

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 16/24 D x ( t )= E x ( t )= F None of the above. Question number 15. You did not answer this question. Wrong. Give the value(s) of a for which the columns in the matrix are linearly dependent. A B

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 17/24 C D E F None of the above. Question number 16. Your answer was C. Correct. Let X be the matrix function Determine if X is a fundamental matrix for system x ' = A x with If so, find the solution of the system that satisfies

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 18/24 A B C D E

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 19/24 F None of the above. Question number 17. Your answer was A. Wrong. Find the general solution to the system x ' = A x where A is the given matrix. A x ( t )= B x ( t )= C x ( t )= D x ( t )=

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 20/24 E x ( t )= F None of the above. Question number 18. You did not answer this question. Wrong. Find the general solution to the system x ' = A x where A is the given matrix. A x ( t )= B x ( t )= C x ( t )=

11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 21/24 D x ( t )= E x ( t )= F None of the above. Question number 19. You did not answer this question. Wrong. Find the general solution to the system x ' = A x where A is the given matrix. A x ( t )=

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 22/24 B x ( t )= C x ( t )= D x ( t )= E x ( t )= F None of the above. Question number 20. You did not answer this question. Wrong. Find the general solution to the system x ' = A x where A is the given matrix.

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 23/24 A x ( t )= B x ( t )= C x ( t )= D x ( t )=

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11/29/23, 11:16 PM ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771… https://ccs.casa.uh.edu/cgi-bin/canvas?course=5554_student_60330a9bed847266529c731eed7e030e6e68cb5ef3c2a70a51b13388eb9844a5&mode=30&whichattempt=192750_19934_1_81f237021abae7771532e682473… 24/24 E x ( t )= F None of the above.

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practice exam 2

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