Prove that the matrices and a a a 0. a 3. a are Similar ( These 2 matrices are not deagonalısable)

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: ✓ 1.6 Each pair of matrices differ by one row operation. Use this operation to compare det(A) with…

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Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

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Q: A, B, C and D are square matrices of the same size. If ABC = ADC, and matrices A and C are…

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Q: If A and B are 2 × 2 orthogonal matrices, show AB is also orthogonal.

A: Let A and B be    orthogonal matrices.We have to show that AB is an orthogonal matrix.We know thatA…

Q: TRUE/FALSE Assume that all the given matrices are n × n. If A = O, but Ak = O (where O denotes the…

A: Given:   To Check: A is singular or not Concept: A is singular only when det(A) = 0

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: Prove that if A and B are two similar n x n matrices, then they have the same determinant and the…

A: (.) Similar matrices: Two  matrices  are  similar if there exists a   non - singular matrix such…

Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

A: To state true or false given statement.

Q: 4. Explain what is wrong with the following "proof" that (ABC)" – C"B" A" for three conformable…

A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: If Q and U are unitary matrices, show that Q-1 is unitary and also QU is unitary. Start from QHQ = f…

A: As per the question we are given two unitary matrices Q, U and we have to show that Q-1 , QU are…

Q: Select all of the following that are true for all nxn matrices A and B. AA²-A²A (A+BILA-B)-A²-B²…

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Q: es m- Exercise 2.3.34 If A and B are n x n matrices, show that: a. AB = BA if and only if (A+B)² =…

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Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: 3. Find m and n so that the matrix below is symmetric:

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Q: 1. Say either true or false in cach of the statements below, and prove cach assertion. (a) The…

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Q: Suppose A,B,C are each nxn invertible matrices. Show (ABC) CBA.

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Q: Let A, B, C and D be invertible n xn matrices with n> 7, which satisfy the equation ABCT DBA"C = ABT…

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Q: 3. Consider the matrices A = |-1 2 2| and B= -1 1 1 -1 -1 (a) Find AT. (b) Compute A². (c) Calculate…

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Q: 47. Prove that if A and B are square matrices and AB is invertible, then both A and B are…

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Q: Determine if the pairs of matrices A and B are similar. (5 1) (3 2) B = 2 1 a) A= 4 5

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…