The n x n lower triangular, upper triangular, and symmetric Pascal matrices are set as Ln, Un and Sn, respectively. In addition, n xn square matrices A, is given by An = Un - In, where In is the nx n unit matrix. | (1) Calculate A (= A5A5) and A (= A5A5A5A5). Just answers are OK. (2) Let us consider the "natural logarithm of a matrix". First, expand Inx as a Taylor series at x = 1. Complete the following equation with clarifying the coefficients C1, C2, C5: In x = c (x – 1) + c2(x – 1)2 + c3(x – 1)3 + C4(x – 1)* + cs (x – 1)5 + . %3D (3) The natural logarithm of square matrix X can be defined as In X = c, (X – 1) + c2(X – 1)? + c3(X - 1)3 + c4(X – 1)* + c5(X – 1)5 + .. with Cn (n = 1,2, ..) derived in (4) and the corresponding unit matrix I. Calculate and give In U5, and then give In L5. A TL (2)
The n x n lower triangular, upper triangular, and symmetric Pascal matrices are set as Ln, Un and Sn, respectively. In addition, n xn square matrices A, is given by An = Un - In, where In is the nx n unit matrix. | (1) Calculate A (= A5A5) and A (= A5A5A5A5). Just answers are OK. (2) Let us consider the "natural logarithm of a matrix". First, expand Inx as a Taylor series at x = 1. Complete the following equation with clarifying the coefficients C1, C2, C5: In x = c (x – 1) + c2(x – 1)2 + c3(x – 1)3 + C4(x – 1)* + cs (x – 1)5 + . %3D (3) The natural logarithm of square matrix X can be defined as In X = c, (X – 1) + c2(X – 1)? + c3(X - 1)3 + c4(X – 1)* + c5(X – 1)5 + .. with Cn (n = 1,2, ..) derived in (4) and the corresponding unit matrix I. Calculate and give In U5, and then give In L5. A TL (2)
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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