Find the characteristic polynomial of the following matrices.[Note: Finding thecharacteristic polynomial of a 3×3 matrix is not easy to do with just row operationsbecause the variable A is involved.]-1(a) 0 4 -11 04 0-1 0 21 01 2(b)32Show that if A and B are similar, then det.Adet B.

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Answered: Find the characteristic polynomial of…

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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Working over R: (a) is it possible to find distinct 2 × 2 matrices A, B which are similar but not congruent? (b) is it possible to find distinct 2 x 2 matrices A, B which are congruent but not similar? Select one: O There is not enough information to answer this question Yes to both O(a) Yes, (b) No O(a) No, (b) Yes O No to both
(a) Show that if A, B,C are matrices such that A has an inverse and such that A- B = A · C then B = C (b) The situation is different if A does not have an inverse: Consider 2 -2 Show that A has no inverse and find two matrices B and C with A - B = A · C but with B + C.
Find bases for row(A) and col(A) in the given matrix using AT. -8 0 3 1 3 1 3 7 -5 1 6 8 row(A) col(A) A = 3 -1 2 11 11 ↓ 1
Linear algebra
Use the fact that matrices A and B are row-equivalent. -2 -5 8 0-17 1 3 -5 1 A = -9 5 -9 7 -13 5 -3 1 0 0 1-2 0 3 0 0 1 0 B = 01-5 0 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. 11
hand written plzzzz
If A = b c d I then A is invertible if ad-bc0, in which case A-1 = If ad bc = 0, then A is not invertible. Find the inverse of the given matrix (if it exists) using the theorem above. (If this is not possible, enter DNE in any single blank. Enter sqrt(n) for √n.) ↓ 1 1 ad - bc -C 5/√2 -5/√2 5/√2 5/√2 d -b |
Assume that the matrices A and B below are row equivalent. Find bases of Col(A) and Null(A). O 21 0 -7 3 -6 0 21 [1 0 -2 0 7 -1 -1 -1 0 1 3 0 0 A B = %3D %3D -2 4 3 1 0 0 1 5 2 -4 4 34 0 0 0 0
Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 1 3 -5 1 A = -9 -21 33 3 -87 7 7 -13 5 -3 1 0 1 0 1 -2 0 0 1 -5 0 0 0 1 B = 3 0 0 0 0 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A.
(a) A = X = (b) A = X = For each of the following, factor the matrix A into a product XDX-¹ where D is diagonal. -2-8 -4 -5 -5 5 0 -1 ده 6 -31 -3 -6 3 1 2 -1 D D || 0 0 0 0 0 0 0 0 0 0 0 0
Matrices D, M and X are 5 x 5 invertible matrices. Given det (A) = 7, det (M) = - 4, and let (P) = 6 find the following. (a) det (3M¹) b) det (A-¹MP-¹)

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Find the characteristic polynomial of the following matrices.[Note: Finding the characteristic polynomial of a 3×3 matrix is not easy to do with just row operations because the variable A is involved.] -1 (a) 0 4 -1 1 0 4 0 -1 0 2 1 0 1 2 (b) 3 2 Show that if A and B are similar, then det.A det B.