Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD. If not, explain why the matrix is not diagonalizable.

Q: Explain why the columns of an nxn matrix A are linearly independent when A is invertible.

A: The objective of this question is to understand the relationship between the invertibility of a…

Q: Can you provide one image or figure of the hermitian matrix?

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Q: Explain on which basis do we use in the Vandermode matrix?

A: The Vandermonde matrix is a matrix that is often used in various mathematical fields, including…

Q: Define bidiagonal matrix.

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Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

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Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: why is the matrix like that?

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Q: What is the Triangular matrix?

A: What is the Triangular matrix?

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 a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Explain why the columns of an n x n matrix are linearly independent when the matrix is invertible.…

A: Solution: To prove that the columns of an n x n matrix are linearly independent when the matrix is…

Q: Explain  column vector of m x 1 matrix?

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Q: Find the 3x3 matrix that induces the described action on R3. Rotates the xy plane by 30 degrees,…

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Q: Why does no 3 by 3 matrix have a nullspace that equals its column space?

A: To show why does no 3×3 matrix have a null space that equals its column space. We know the…

Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

Q: Show that the inverse of a nonsingular lower triangular matrix is lower triangular.

A: We have to prove that inverse of a nonsingular lower triangular matrix is lower triangular.

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: To illustrate the multiplication of matrices, and also the fact that matrix multiplication is not…

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Q: Show that every diagonalizable matrix has a square root.

A: Square Root Matrix of a Diagonalizable Matrix is Diagonalizable. A is diagonalizable. Therefore,…

Q: Show that the matrix; is singular

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Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Show that the matrix below does not have an LU-factorization.

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Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

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Q: Show that for a square matrix A, AAT is a symmetric matrix.

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Q: Can you only use matrix, not wronskian. Also indicate what method of matrix was used.

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Q: Let A is a 4 x 4 matrix such that Ar=0 has non trivial solutions. Is the matrix A invertible?…

A: If the equation Ax = 0 has non-trivial solutions, the matrix A is not invertible.Explanation:Steps…

Q: describe how LU factorization of a nonsingular matrix B can be found using Doolittle’s method.

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Q: True/False: Suppose a non-zero n x n matrix A satisfies A³ = 0 (the zero matrix). Then A is not…

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Q: True or False? Suppose A is an 7 x n matrix. If there is an 7 x n matrix D such that AD = I, then…

A: True. This is a property of invertible matrices, which are square matrices that have an inverse. If…