Let M2(R) be the set of 2 x 2 matrices with real number entries, i.e., - {[: :] 1ah ader}. b M2(R) = la, b, c, d e Define matrix addition and matrix multiplication in M2(R) as follows b1 di b2 d2 a1 + a2 b1 + b2 Ci + c2 d1 + d2 a1 a2 C1 C2 b1 di b2 d2 a1a2 + bịC2 a¡b2 + bịd2 Cia2 + dịc2 cıb2 + d1d2 a1 a2 C1 C2 1. Show that M2(R) is a ring under addition and multiplication defined above. [No need to show matrix addition and matrix multiplication are binary operations in M2(R).]

Let M2(R) be the set of 2 x 2 matrices with real number entries, i.e., - {[: :] 1ah ader}. b M2(R) = la, b, c, d e Define matrix addition and matrix multiplication in M2(R) as follows b1 di b2 d2 a1 + a2 b1 + b2 Ci + c2 d1 + d2 a1 a2 C1 C2 b1 di b2 d2 a1a2 + bịC2 a¡b2 + bịd2 Cia2 + dịc2 cıb2 + d1d2 a1 a2 C1 C2 1. Show that M2(R) is a ring under addition and multiplication defined above. [No need to show matrix addition and matrix multiplication are binary operations in M2(R).]

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 41EQ: In general, it is difficult to show that two matrices are similar. However, if two similar matrices...

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Similar questions

Show that the matrix below does not have an LU factorization. A=0110
In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .
Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

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