Determine whether A is diagonalizable. If it is, identify an invertible matrix P, such that A is diagonalizable and find P-'AP

Q: If A be an n x n invertible matrix. Prove that the transpose of A is also invertible.

A: A square matrix is invertible matrix if its determinant is nonzero. To obtain the transpose of the…

Q: Prove that if matrix A is diagonalizable, then AT is diagonalizable.

A: We have given a matrix A, that is diagonalizable.

Q: Given a square matrix A, prove that A is invertible if and only if ATA is invertible.

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Q: If A is an invertible matrix that is orthogonally diago­nalizable, show that A-1 is orthogonally…

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Q: Show that if A is a symmetric matrix, then AT is symmetric.

A: we have to show that if A is a symmetric matrix, then AT is symmetric.   as we know that a matrix B…

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Show that if A is any mxn matrix, then Im= A.

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Q: Under what conditions will the diagonal matrix be invertible? Assume that A is invertible and find…

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Q: determine an orthogonal matrix S such that ST AS = diag(λ1,λ2,...,λn), where A denotes the given…

A: As a first step we need to find the eigenvalues and eigenvectors:

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: 5. Find a dlagonalizes the fouowing natrlx A, and determine the diagonal matrix D = p'AP matrix p…

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Q: If A and B are invertible matrices, show that AB and BA are similar.

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Q: Find a matrix P that orthogonally diagonalizes A. Verify that PTAP gives the correct diagonal form.

A: Given that, First, we have to find eigenvalues and eigenvectors of the given matrix. For eigenvalue…

Q: Show that if A is an orthogonal matrix, then A−1 is orthogonal.

A: Explanation: Given that,  A is an orthogonal matrix.

Q: whether the matrix is in reduce

A: The matrix is given as  , 190-10001500000100000 1. The condition for row echelon form (ref) is The…

Q: Find x such that the matrix A is nonsingular.

A: Given: The inverse of a matrix is given as follows,

Q: If A is an orthogonal matrix, find a QR factorization of A

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Q: 0.5(In+A) and 0.5(In-A)

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Q: * Let A be and m x n matrix. Describe the matrix E such that EA is A with row swapped.

A: Given matrix A is a m×n matrix. And the elementary matrix E and EA are row swapped. Since elementary…

Q: Show that if A is a symmetric nonsingular matrix then A−1 is also symmetric.

A: A is a symmetric non singular matrix, which means inverse exists and

Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

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Q: Let A be an m x n matrix. Is ATA symmetric? Explain.

A: Given that, A is an m×n matrix

Q: For what values of λ ∈ R is the matrix invertible

A: The matrix A is invertible if and only if its determinant is non-zero.

Q: If A is diagonalizable such that A= XDX-!, then the diagonalizing matrix X is unique. Select one: O…

A: Given that A is diagonalizable and A=XDX-1 Now, the matrix X is formed by the eigen vectors of the…

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: If A is a symmetric matrix, does it follow that the transpose of matrix A is also symmetric?…

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Q: In the LU decomposition of the matrix if the diagonal elements of U are both 1, then the lower…

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Q: If A is diagonalizable such that A = XDX, then the diagonalizing matrix X is unique. Select one:…

A: Given that A is diagonalizable. S.t. A=XDX-1

Q: Show that if A is an upper triangular matrix, then AT is lower triangular.

A: Given, A is an upper triangular matrix

Q: Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the correct…

A:

Q: If A is an invertible matrix that is orthogonally diagonalizable, show that A-1 is orthogonally…

A: Let the orthogonal decomposition of A be denoted as A = QTDQ where Q is orthogonal and D is…

Q: IF A is diagonalizable such that A XDX, then the diagonalizing matrix X is unique. %3D Select one: O…

A: Given A is diagonalisable and A = XDX-1

Q: Show that if the matrix X is diagonalizable, then X" is also diagonalizable.

A: Given that the matrix X is diagonalizable. We have to show that XT is also diagonalizable. Since,…

Q: Find a matrix P that orthogonally diagonalizes A. Verify that PTAP gives the correct diagonal form.

A:

Q: Let A be an m xn matrix. Explain why the matrix ATA is symmetric.

A: A square matrix is symmetric if  A^T = A

Q: Explain why for any matrix A, AA' exists and prove that AA' is a symmetric matrix

A: Let A is any matrix of order m by n Am×n    and   Atn×m Now  AAt exists of order m by m To prove…

Q: Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A…

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Q: If A is any matrix, show that both AAT and ATA are symmetric.

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Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

A: Given: A=1011

Q: Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P =…

A: First we need to find eigen values:

Q: (b) Show that an n x n complex matrix is unitarily diagonalizable if and only if it is normal.

A: By using Schurs theorem the answer is given as follows :

Q: If AC is an invertible matrix, then show that A is also an invertible matrix

A: Given- AC is an invertible matrix, i.e.- ACAC-1=I⇒ACA-1C-1=I⇒AA-1CC-1=I

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

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Q: If A is a symmetric matrix, then At = A Diagonal Matrix TAI

A: A is a symmetric matrix

Q: If A EM,C {c} such that A2 = A. Prove that A is not a strictly diagonally matr. the last word is…

A: A square matrix is said to be strictly diagonally Matrix if all entries are zero except diagonal…

Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix