B-60and B =-1 1 16A =3-3 1-14 -3Check all of the reasons that A and B are not similar matrices:A. Al is lower triangular and B is upper triangular.B. A is invertible but B is not, or vice-versa.C. A and B have different determinants.D. A and B have different ranks.E. A and B have different eigenvalues.F. A and B have different characteristic polynomials.

If determinant of A square matrix is nonzero, then A is invertible. If two matrices A and B are…

Answered: A: 3 -3 -1 0 0 1 1 0 and B 16 4 [ 0 0…

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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Let A and B be 3 x 3 matrices such that A 3 = B 6 l10. The matrix C = A – 2B is invertible. [5] (A) True (B) False
2. Consider the matrix A = [10 -3 0 1 00 3 (a) Find elementary matrices E₁ and E2 such that E2E₁A = I. (b) Write A-¹ as a product of two elementary matrices. (c) Write A as a product of two elementary matrices.
Determine whether each of the following matrices is positive definite. If it is not, give a submatrix and determinant that demonstrates this. 0 3-2 3 -1 3 -2 3-2 A₁ = A₂ = 1 1 1 -2 4 -3 19 3 -2 -3 1 -3 3 A3 = -3 12 -1 3 -1 -3 A₁ is positive definite A₁ is not positive definite:
Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini
Let A and B be 3 x3 matrices, with det A = 2 and det B = 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det B". det B" (Type an integer or a fraction.) d. Compute det A-1. det A (Type an integer or a simplified fraction.) e. Compute det A. 3 det A° = (Type an integer or a fraction.)
Show that A and B are not similar matrices. (Enter your answers as comma-separated lists.) A = 6 1 9 0 6 7 0 0 9 , B = 1 0 0 −1 9 0 6 7 9 Since A has eigenvalues ? = and B has the eigenvalues ? = , the two matrices are not similar.
A = 1+ 2-i 9 B = 1 1 1 1 10 0 0 1 0 0 1 1 002 Invertibility of B: C = = 1 3 1 2 3 2 (Entries of C are from Z9). 85 1 Note that only the entries of matrix C are in Z9. The other two matrices A and B are matrices with real numbers entries. (a) Find the inverse of all the given matrices, if they are invertible, using Gauss-Jordan method? Invertibility of A:
A and B arenxn matrices. Check the true statements below: A. An elementary row operation on A does not change thé determinant. B. The determinant of A is the product of the diagonal entries in A. C. (det A)(det B) = det AB. D. If 1+5 is a factor of the characteristic polynomial of A, then 5 is an eigenvalue of A.
A is invertible iff there exists a matrix B so that AB = BA = I. It is simple to show that: (i) If A is invertible and AB = I, then BA = I as well and B is the unique such matrix. (ii) If A is invertible and BA = I, then AB = I as well and B is the unique such matrix. This shows that if A is invertible, then there is a unique matrix B such that AB = I or BA = I. Call this unique matrix A−1 . The goal here is to show that the assumption “A is invertible” is not needed in (i) or (ii). Prove: Let A and B be square matrices with AB = I. Show that A is invertible and hence B = A−1 . You may refer to Theorem 1.5.2 or Theorem 2.2.2, but be clear and complete in your argument.
Given 2 x 2 matrices A and B such that 5 0 = [68] 05 AB = BA OB is noninvertible O B-¹ = A OB¹1=5A OB¹ = A what is the inverse of B?
Which of the following matrices has the same determinants? [3 10 15 7 0 19 12 0 - 12 1 4 7 A=0 0 1 000 LO 0 0 0 4 1 0 10 7 8 0 039 C= 0 0 3 -9 1 0 0 0 1 7 ¹0 000 B= B: 0 0 0 0 00 2 00 54 - 320 L21 0 4 21 3- 1 0 13 09 0 3 1 05 7 0 3 81 4 0 - 3 1 2 7 0 2- D=002 000 0 0 0
If A = a b c d " then A is invertible if ad bc # 0, in which case A-¹ = 27 4 1 ad - bc If ad bc = 0, then A is not invertible. Find the inverse of the given ↓ 1 d -b -C a matrix (if it exists) using the theorem above. (If this is not possible, enter DNE in any single blank.)

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