Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) A= 5 0 0 0 1 3 0 3 1 (D,Q)

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A: Eigen vector for:  Is:  With eigen values 7 and -2.

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

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

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Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P"AP gives the proper…

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Q: Exercise 2. Let A be an n x n matrix. Show that if A is similar to a diagonal matrix, then so is AT.

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

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Q: a. Which of the matrices are orthogonal (has orthonormal columns)? V3 -2 V2 V3 [1 1 -4] -2 1 Find…

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Q: (a) Considering an 3 × 3 Suppose, invertible and symmetric matrix A, prove that A−1 is symmetric.…

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A: First reduce into echelon form then find basis of row space, as in next step.

Q: Orthogonally diagonalize ATA and determine the matrix P which orthogonally diagonalizes ATA.

A: Given matrix is A=32232-2 So AT=32223-2 Now ATA=32223-232232-2⇒ATA=9+4+46+6-46+6-44+9+4⇒ATA=178817…

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Q: 3 0 0 3 5 21 0 0 0 1 4 1 2 2 0 |0 0 2 1 3 0 1 2.

A: The given matrices are, 300010002, 352412132,100020001

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Q: Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A…

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Q: Prove Theorem . If A is an invertible matrix, then A is invertible and

A: If A is invertible, then AT is invertible and (AT )-1  = (A-1 )T . To prove, (AT)-1=(A-1)T  We need…

Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper…

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Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper…

A: Given A=4444Characteristic equationA-˨I=04-˨444-˨=04-˨-16=016+˨2-˨-16=0˨2-8˨=0˨=0,8

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Q: (a) Define orthogonal and idempotent matrices with examples. Prove that the only matrices which…

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Q: Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let (2)…

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