In our course, you may have noticed that we mainly talked about orthogonally diagonalizing a matrix A E Maxn(R). What if we wanted to determine whether an arbitrary matrix A E Maxn(C) is orthogonally diagonalizable? In other words, if A € Mnxn(C), when can we find a diagonal matrix D e Maxn(C) and matrix PE Mnxn(C) such that PT = P-, for which D = P-AP? What parts of our discussion of unitary diagonalization still work, and which parts break down? Is every complex symmetric matrix orthogonally diagonalizable? Are there non-normal matrices that are orthogonally diagonalizable?

Q: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix, a. Is GH defined? If so, what is the order…

A: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix,a. Is GH defined? If so, what is the order of…

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A: We are given that a 6x3 matrix A has rank 3. So, dim(Row A) = 3. We know that dim(A) = dim(Row A) +…

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Q: |a b X y m nl

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A: If a matrix A is non-singular then all the rows and all the columns  of A are linearly independent.

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A: We have to solve given problem:

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Q: if A is m xN matrix pivot in every row, then Ax-b has that has a a unique solution for each b in Rm

A: The given question can be solved as shown in step2.

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A: We will use the knowledge of standard value decomposition (SVD) of a square matrix.

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A: To determine: If there is more than one correct outcome to a matrix in row echelon form. If each row…

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A: We will use the basic knowledge of LU decomposition to answer this question.

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Q: For skew anti-symmetric matrix, the sum of its entries is (A 1 В -5 10 E -1

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Q: if the column sums of a matrix C are all strictly less than 1, then the inverse of the matrix I-C…

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Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

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