Answer all the questions: (2 1 1 1. The characteristic polynomial of the matrix 0 1 0) is A1 1 2. a) 23 - 522 + 71- 3 b) -13 + 522 - 72 +3 c) -23 + 522 d) None of these

Q: Find the characteristic polynomial of the matrix 5 A 0 -5 -1 -4

A: Characteristic polynomial is obtained using the expression |A-λI|, where I is the identity matrix.

Q: (b) Find the characteristic equation of the matrix P defined by [2 1 1] P = 1 2 1 li 1 2] Further…

A: The given matrix is P=211121112 the characteristic equation is given by P-λI=02-λ1112-λ1112-λ=0…

Q: Write down a set S of matrices such that every square matrix whose characteristic polynomial splits…

A: We know that, If A is n×n square Matrix then Jordan Canonical Form(JCF) of A  is similar to A. Let S…

Q: 15. Suppose that the characteristic polynomial of some matrix A is found to be: p(a) = (λ— 4)³ ((A −…

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Q: 2. Show that the following is a basis for M, 2x2 [3 6 3 1 0 -1 2 -8 12

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Q: Find the characteristic polynomial of the matrix, A= (3−12−624−312),then verify Cayley-Hamilton…

A: We have to find A inverse

Q: 8. Find a basis for the null space of 2 1 0 A = 3 2 1

A: To find basis of null space,  Ax=0 Firstly reduce the augmented matrix in reduced echleon form, then…

Q: 5 4 2 3. Consider the matrix A = 4 5 2. 2 2 2 (a) Find the characteristic polynomial det(A– AI) = 0,…

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Q: Suppose that the characteristic polynomial of a matrix A is p(A) = A(A² − 6A + 9). A will have…

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Q: 7. (1 -- Consider the symmetric matrix S = Find an orthogonal matrix Q such that Q" sQ = 8 ]-

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Q: Let Q be the n × n real matrix in which each entry is 1. Show that det(Q−nIn ) = 0.

A: Given:         Q=11....111....1....................11....1n×n,…

Q: 4. Exercise §5.2 #20 [This exercise presen Theorem 5.9 using the Möbius Inversion Form to that in…

A: Given, d be a positive divisor of p-1. To prove that                            f(d)=ϕ(d)

Q: 5 2 1 What is the coefficient of X? in the characteristic polynomial of the matrix A = 1 1 2 ? 15 2

A: Given : 5211127152

Q: Pls explain to me step by stepThanks

A: The given matrix is

Q: 2. If the characteristic polynomial of a matrix A is p(2) = 23 - 522 + 62. Then tr(A) = None -5 O 1

A: Solve

Q: The Cayley-Hamilton Theorem states that a matrix A satisfies its own char- acteristic equation. That…

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Q: Suppose A is an n × n nonsingular matrix. Prove that there exists a polynomial q(x) such that A-1 =…

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Q: Find an orthonormal basis [b₁,b2, b3] of spam[13] where B = {(1,0,1), (1,0,-1), (0₂1. 2)}, using the…

A: Please follow the next step.

Q: Show that the characteristic polynomial of A is p(λ)=λ2−5λ+6.

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Q: Let A be a 2 ×2 matrix and let p(λ) = λ2 + bλ + c be the characteristic polynomial of A. Show that b…

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Q: $5.5, Exercise 4. Find a basis for the null space of 0 -1 A = -1 4 -5 1 -2 What is the dimension of…

A: The given matrix is A=10-121-1004-51-2. First convert the above matrix into reduced row echelon form…

Q: .18 Find the characteristic polynomials and the minimal polynomials of the followi matrices: 시 1 1 1…

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Q: Find the characteristic polynomial of the matrix 3 -5 A = 1 -2 -5 3 2(x) =D

A: Given,            A=3-5001-2-530

Q: Find the characteristic polynomial of the matrix -9 A = 1 p(z)

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Q: 7. Suppose A Matnxn (F) is a matrix with det(A) #0. Prove that Espan{Id, A, A²,..., An-1}. A

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Q: Let A be an n x n matrix such that Am = 0 for some positive integer m. Show that A is not…

A: A is a n×n invertible matrix, such that Am=0⋯⋯1 Taking determinants both side, detAm=det0detAm=0…

Q: 2. Compute the minimal polynomial of the following matrix (with coefficients in R) WITHOUT comput-…

A: We have to find the minimal polynomial of the given matrix M=-1033-1856-1865. Let M2+aM+bI3=0 where…

Q: 11. Prove that similar matrices have the same characteristic polynomial.

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Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 7A +…

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Q: 8. Find a basis for the null space of 2 A = 2

A: As per guidelines we are  supposed to solve only first Question for second Question kindly ask it…

Q: Use triangular matrix method to find det(8). DO NOT use co-factor expansion -2 -3 -2 1

A: We need to find the determinant of the matrix B=1-11001041-2123-3-21 Let R1, R2 ,R3,  R4 denote the…

Q: Be A matrix 2×2 and pA the respective characteristic polynomial. Knowing that pA(A)=0, prove that…

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Q: Find the characteristic polynomial of the matrix p(x) = || 5 -2 0 419 A = 0 -4 0

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Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 2A +…

A: Finding such a is equivalent to finding a 2 by 2 matrix with trace -2 and determinant 5. As in…

Q: Let A be a 4 × 4 matrix and suppose that A is a diagonalizable. If the characteristic polynomial of…

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Q: 1. If the characteristic polynomial of a matrix A p(2) = 23 + 2² – 62. Then tr(A) O 1 None -6 O -1 5

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Q: 4. Find a basis of the nullspace of 2 -6 5 -8 A = 1 -3 1 -1 3 -9 4 -5

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Q: Prove that P-1 = P" if and only if the columns of P for an orthonormal basis for R" for P n n.

A: We have to prove that P−1=PT if and only if the column of P for an orthonormal basis for Rn for…

Q: 5 3. Consider the matrix A = 45 2. |2 2 2 (a) Find the characteristic polynomial det(A– AI) = 0, and…

A: Given: Consider the matrix A A=542452222

Q: 17. Find a basis for W-, where 2 W = span 3 7 4 8

A: We have W=span1234, 5678 The basis for W⊥ is the null space of the matrix formed by the rows made of…

Q: 2 17 1 12 7 15 2] What is the coefficient of X in the characteristic polynomial of the matrix A =…

A: Given matrix 5211127152Form a new matrix by subtracting λ from the diagonal…

Q: Find the characteristic polynomial of the 3 x 3 matrix, A, where

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the number of…

Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x?,1 + x + 4x²,1 – 7x

A:

Q: Suppose that a matrix M is nilpotent if exists an x element of Z+ in where Mx = 0. If M is…

A: We will prove the given result.

Q: 2. If the characteristic polynomial of a matrix A is p(2) = 23 – 522 + 62. Then tr(A) = None -5 11…

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Q: 3.) Apply the Gram-Schmidt orthonormalization process to the basis B = {1,t, t²} in P2 using the…

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Q: Determine the number of distinct characteristic polynomials of matrices in M2×2(Z2).

A: This can be done as follows:

Q: 39. Find an orthonormal basis 1, 2, 3 of R³ such that (G) span

A: Given,                        spanu1→=span123and        spanu1→, u2→=span123, 11-1

Q: 2) - Dr. M of the following is the characteristic polynomial of the matrix A = Select one: p(X) = X2…

A: We have to solve