3.3.47. True or false: If B = S-i AS are similar matrices, then II Bloo-llAlloo.

Question

Question

math algebra

Answer 1

Answer #1

True.

If 2 matrices are similar then their determinants will be equal.

determinant(B)= determinant(S⁻¹)x determinant(A)x determinant(S)

Implies, determinant(B)= determinant(A)

Implies, determinant(S⁻¹) x determinant(S) =1

Answer 2

Similar Homework Help Questions

True or false. Please justify why true or why false also (I) A square matrix with...

True or false. Please justify why true or why false also (I) A square matrix with the characteristic polynomial 14 – 413 +212 – +3 is invertible. [ 23] (II) Matrix in Z5 has two distinct eigenvalues. 1 4 (III) Similar matrices have the same eigenspaces for the corresponding eigenvalues. (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geo- metric multiplicity is 3. (V) Two diagonal matrices D1 and D2 are similar if...
We say that A and B are similar matrices if A = SBS-1 for some invertible...

We say that A and B are similar matrices if A = SBS-1 for some invertible matrix S. Are the following true or false. Given a mathematical reason (proof). (a) If A and B are similar, then A and B have the same eigenvalues. Answer: (b) If A and B are similar, then A and B have the same eigenvectors. Answer: c) If A and B are similar, then A - 51 and B – 51 are similar. Answer: (d)...
Help! Let B and C be similar nxn matrices. Prove that the matrices given by: I...

Help! Let B and C be similar nxn matrices. Prove that the matrices given by: I +5B - 2B4 and I +5C - 204 are similar. (6 pts)

True or False? The probability of a Type I error (a) and Type (II) error (B)...

True or False? The probability of a Type I error (a) and Type (II) error (B) are complementary and total to 1. a. True b. False
let a and b be n*n similar matrices, namely, B=S^-1 AS. show that the matrices a...

let a and b be n*n similar matrices, namely, B=S^-1 AS. show that the matrices a and b have the same characteristic polynomial, det(a-λI)=det(b-λI) and, consequently, the same eigenvalues.
(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is...

(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is an n×n invertible matrix and AB is an n×n invertible matrix, then B is an n × n invertible matrix, for all natural numbers n. [4 marks] (iii) det(A) = 1 for all invertible matrices A that satisfy A = A2....

Determine if the statements are true or false. 1. If A and B are nxn matrices...

Determine if the statements are true or false. 1. If A and B are nxn matrices and if A is invertible, then ABA-1 = B. ? A 2. If A and B are real symmetric matrices of size nxn, then (AB)? = BA 3. If A is row equivalent to B, then the systems Ax = 0 and Bx = 0 have the same solution. ? A 4. If, for some matrix A and some vectors x and b we...
Chromosomal rearrangement occurs via meiosis I and meiosis II a. True b. False c. They are...

Chromosomal rearrangement occurs via meiosis I and meiosis II a. True b. False c. They are both correct d. None is correct The nucleotide sequence of RNA is? a. A-U-T-C b G-C-U-T c A-C-T-X (this CANNOT BE CORRECT!) d A-U-G-C e None of the above is true A genotype of Nn denotes of heterozygote genotype a. True b. False c. Both a and b are correct d. Both a and b are incorrect Sickle cell hemoglobin is an example of...
QUESTION 14 True or False: The following two polygons are similar. B E 109 D 41°...

QUESTION 14 True or False: The following two polygons are similar. B E 109 D 41° 30° 30° А с F True O False QUESTION 15 True or False: The following two polygons are similar. R 5 S Х 5 120° 60° 3 3 3 3. 60° 120° Z 5 Q 5 T W OO True False

just give one or two examples of similar matrices 4. For each of the following matrices...

just give one or two examples of similar matrices 4. For each of the following matrices A, find a "model" matrix B such that A is similar to B. (a) ( 21 o) (b)(i ).