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3. Consider the following 3x3 matrices A, B,C, D, and E. A has a determinant of 10. B can written as a product of 5 elementary matrices. The product r(C)n(C) is greater than 0. The row of D form a basis for R. E has eigenvalues 1,2, and 3.

3. Consider the following 3x3 matrices A, B,C, D, and E. A has a determinant of 10. B can written as a product of 5 elementary matrices. The product r(C)n(C) is greater than 0. The row of D form a basis for R. E has eigenvalues 1,2, and 3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Consider the following 3x3 matrices A, B, C, D, and E. A has a determinant of 10. B can written as a product of 5 elementary matrices. The product r(C)n(C) is greater than 0. The row of D form a basis for R. E has eigenvalues 1,2, and 3. (a) If you know for a fact that det(A) + det(B) = det(C), What is the deter- minant of matrix (AB)-2? (b) How many solutions are there to the linear equation EX = V, for any I x1 vector V? (c) What is the product of the eigenvalues of the matrix ACE? (d) Solve for E in terms of A, B, C, and D: (A²)(D-3)(det(B))(E)+(C)(D²)(B³) = 0.
Transcribed Image Text:3. Consider the following 3x3 matrices A, B, C, D, and E. A has a determinant of 10. B can written as a product of 5 elementary matrices. The product r(C)n(C) is greater than 0. The row of D form a basis for R. E has eigenvalues 1,2, and 3. (a) If you know for a fact that det(A) + det(B) = det(C), What is the deter- minant of matrix (AB)-2? (b) How many solutions are there to the linear equation EX = V, for any I x1 vector V? (c) What is the product of the eigenvalues of the matrix ACE? (d) Solve for E in terms of A, B, C, and D: (A²)(D-3)(det(B))(E)+(C)(D²)(B³) = 0.
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