Re-express the matrix B in diagonalised form B = 0" DO, where O and D are orthogonal and diagonal matrices respectively.

Q: Let A be symmetric matrix. Then two distinct eigenvectors are orthogonal. true or false ?

A: Applying conditions of symmetric matrices we have

Q: Determine whether the matrix is orthogonally diagonalizable.

A:

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

A:

Q: If A and B are nXn diagonalizable matrices, then A+B is also diagonalizable. True or False? Give an…

A:

Q: Show that the matrix is not diagonalizable.

A:

Q: State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c) diagonal,…

A:

Q: Prove Any n by n triangular matrix with main diagonal entriesare all 1 is diagonalizable if and only…

A: Triangular Matrix: A triangular matrix is a square matrix where all the values above or below the…

Q: Show that the product of two orthogonal matrices is also an orthogonal matrix. Is the product of two…

A:

Q: Calculate the matrix P, the matrix D, det(P), and the matrix P! Is the matrix A2 diagonalizable?…

A: Solution:-

Q: 2) does the following matrix is orthonormal and orthogonal? Why? R = 2

A: Orthogonal and orthonormal matrix

Q: Prove the theorem: AAT is a symmetric matrix for any matric A.

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

A: .

Q: Find an orthogonal matrix Q and a diagonal matrix D

A: Follow the procedure given below.

Q: Let I be the identity matrix of nxn. Please Compute the matrix fuunctions COST I

A:

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: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: VýB × VA

A:

Q: Let Q be a matrix with orthonormal columns, then QQT = 1. :Select one True False

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Q: 2 0 -1 2 0 0 1 1

A:

Q: Prove Theorem For any matrix A, AAT and ATA are symmetric matrices.

A: To Prove for any Matrix A, AAT and ATA are symmetric matrices.   A matrix X is symmteric if XT=X.…

Q: 4. Prove that the product of two upper triangular matrices is always another upper triangular…

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Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

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Q: Determine the inverse matrix of matrix C.

A:

Q: Show that if A and B are orthogonal matrices, then ABis an orthogonal matrix.

A: Given: A and B are orthogonal matrices. Therefore, AAT=I=ATA and BBT=I=BTB     . . .(1)

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

A:

Q: Let us consider a square matrix A of order n with Eigen values of a, b, c then the Eigen values of…

A:

Q: If A and B are nXn diagonalizable matrices, then A+B is also diagonalizable. True or False? Give an…

A: Given statement, If A and B are n×n diagonalizable matrices, then A+B is also diagonalizable.

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Let A be annxn matrix and B=A+T, where / is the identity matrix, then it is possible for A and B to…

A: Given matrix combination is B = A + I

Q: Find the singular values of the matrices in Exercises

A:

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

A: Given that, A is an m×n matrix

Q: a) Prove that Hermitian, skew-Hermitian, and unitary matrices are normal.

A:

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: Determine whether the matrix is orthogonally diagonalizable.

A:

Q: Determine whether the following statement is true or false. Justify your answer in both case. (Type…

A: Answer

Q: Let A = [0 1 0 0 ], A^(-1) is equal to: * Does not exist Identity matrix Null matrix

A:

Q: Find the singular values the matrix:

A: A singular value of a real matrix A is the positive square root of an eigen value of the symmetric…

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: The multiplicative identity matrix of order 2 is I2 =_______.

A:

Q: Find SVD for the matrix A=[1 2;2 1].

A:

Q: Find a matrix P that diagonalizes 1 0 0

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). 3 -4 -3 L = U = A,

A: The solution is given below

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A:

Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: 1 Determine whether the matrix C = is an orthogonal matrix. 1

A:

Q: Find the rank of matrix using Daussian elemination  method. A=[1 -1  2 , -3  3  -6 , 0  1  2]

A: NOTE: It is not "Daussian elemination  method", it is "Gaussian elemination  method".

Q: State whether the matrix is diagonalizable or not. [:] 0 7 0 0 O diagonalizable O not diagonalizable

A: Given matrix is 0700 and now subtract λ from the diagonal elements=0-λ700-λThe determinant is…