16:39 ✓+27 66 466 47742 minutes agoIf the minimal polynomial of a matrix A is (2) -- then A is a scalar matrix k. (I is the identity matrix)O TrueO False=|||Vol) 4GLTF2 all 55%O<:

Answer : TRUE Important points on minimal…

Answered: If the minimal polynomial of a matrix A…

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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А В Let the 4 x 4 matrix M is written as 2 × 2 block matrices in the form M where A, B, D are 2 × 2 matrices and 0 is the 2 × 2 zero matrix. Prove that det(M) det(A) det(D). IE M = ( A where A, B, C, D are 2 × 2 matrices, then can you say det(M) = C D det(A) det(D) – det(B) det(C)? Justify your answer.
Show that every scalar matrix is symmetric.
Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A as long as it is a square matrix.
(2) Find the examples that satisfy the statement in the given items and show some work how they are correct examples (a) A 4 x 4 matrices A that is not digonalizable. (b) (c) Two matrices A and B that have the same characteristic polynomial but are not similar. Two diagonal matrices D₁ and D₂ that are similar but they are not equal. (d) Two similar matrices A and B such that A is orthogonally digonalizable but B is not orthogonally diagonalizable.
Let A B denotes the tensor product of matrices Amxn and Bpxq defined by the block matrix A B = a12B 922B a11B a21 B : : ami B am2 B : ain B a2n B : amn B mpxnq (a) Let A, B, C, D be defined as Amxn, Bpxq, Cnxk, and Dqxr. Prove that (AB)(C > D) = ACⒸ BD (b) Let Amxm and B₁xn be nonsingular matrices. - Prove that (AB) is nonsingular. - Find the inverse matrix of (AB) (c) Prove that the following equality applies for any Amxm and Bnxn square matrices trace(AB) = trace(A) * trace(B)
Let x=(4,3, 1, 1) and y (8, 2, 7, 1). Determine which of the following statement(s) is/are true: (i) xy is a scalar (ii) xy" is a matrix (iii) yx is a matrix (iv) xyx is a vector O a. (ii), (i) and (iv) only O b. (i), (ii) and (iv) only Oc. All of the above O d. (i), (ii) and (iii) only.
Questi Suppose A is a 4x4 matrix such that the second and third column are scalar multiples of each other. Then A is not invertible. True O False

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If the minimal polynomial of a matrix A is (A)-- then A is a scalar matrix k. (I is the identity matrix) True O False