Suppose that A and B are orthogonal (n x ) matrices. Show that AB is an orthogonal matrix.

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: Let Q be an orthogonal matrix such that QA makes sense. Show that A and QA have the same singular…

A: Let,

Q: If A and B are orthogonal n by n matrices, then AB is also orthogonal. True or False? Give an…

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Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: Determine whether the given matrix is diagonalizable 3 1 A = 0 1 3

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Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: For any 3x3 matrices A & B: Verify that (AB)" = B" A".

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Q: Find matrices P and D so that A = PDP1 and D is a diagonal

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Q: Suppose A. B and X are 'nxn matrices such that A and B are invertible, and Which one of the…

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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: Show that if A and B are two n × n matrices with the same diagonalizing matrix X, then AB = BA.

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Q: Which of the following matrices is not in Row Echelon Form (REF)?

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Q: If A and C arę nxn invertible matrices and B is an nxn matrix, then

A: By Theorem we can say that

Q: Assuming that b # 0, find a matrix that orthogonally diagonalizes a= [: :] P

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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: 6. Show that if Q is an orthogonal matrix, then 1 0 %3D 0 Q is also an orthogonal matrix.

A: We have to show that HHt = I

Q: Let A and B be n × n matrices. Show that if AB is nonsingular, then A and B must be nonsingular.

A: Matrix: Let Ab is nonsingular. Therefore ABx=0 has only the trivial solution. Now let b be singular…

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

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Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

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

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Q: Suppose that A is an m×n matrix in which no two columns are identical. Prove that A∗A is a diagonal…

A: Given that A is an m*n matrix in which no two column are identical.Since A*A is defined only if A…

Q: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: Let A and B be matrices such that the product AB is defined. Show that if A has two identical rows,…

A: Let A = [aij] be an m×n matrix and B = [bij] be an n×l matrix. Let C = AB = [cij] be an m×l product…

Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: Show that the matrix is not diagonalizable.

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: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: If both matrices A,B are orthogonal prove that (ab) is also orthogonal

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Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: Prove that if the diagonal entries of a diagonal matrix are permuted, then the resulting diagonal…

A: Permuting the diagonal entries of a diagonal matrix D amounts to permuting the rows of that matrix…

Q: Let A, B and C be 2x2 matrices that are invertible under matrix multiplication. Simplify (A CBC)as…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Consider the following matrix: A-() 1. Determine whether A is diagonalizable over C. If so,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose A-A, where A is the matrix. The det (A) is

A: Determinant of a null matrix is equal to zero.

Q: If A and B are orthogonal nxn matrices, then AB-1 is an orthogonal matrix. True False

A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

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

A: Given, A is an upper triangular matrix

Q: Let A be an m × n matrix. Explain why the matrix multiplications ATA and AAT are possible.

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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: Suppose A = UDVT where U and V are n x n matrices with the property that UTU = I and %3D vTV = I,…

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Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: Show that if A is an orthogonal matrix, then AT is also orthogonal.

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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: 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

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…