4. If X is a square matrix, and X has partition where A is an invertible submatrix of X, then where A = X = det (X) = det (A) det(X/A). Here, X/A = D-CA-¹B is the Schur complement of A in X. Use this principle to find the determinant of (²3) X A B C D A B) ₁ CD = 12 1 3 23 2 5 13 1 2 (3 7 - −1 1

4. If X is a square matrix, and X has partition where A is an invertible submatrix of X, then where A = X = det (X) = det (A) det(X/A). Here, X/A = D-CA-¹B is the Schur complement of A in X. Use this principle to find the determinant of (²3) X A B C D A B) ₁ CD = 12 1 3 23 2 5 13 1 2 (3 7 - −1 1

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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