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: 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: 'm confused as to the definition of column space. Looking at this exercise, my understanding is that…

A: Let A∈Fm×n where F is a field. We have seen N(A), the nullspace of A, is given by {x∈Fn:Ax=0} The…

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

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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: 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 why the matrix 80] A B 0 A is not diagonalisable.

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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: 9. A = -2 2

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Q: Let U be an n × n non singular matrix with non zero diagonal entries. Explain why U must be non…

A: Consider the provided question, Let U be an n x n non-singular matrix with non-zero diagonal…

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: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

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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: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

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: Does matrix multiplication commute? That is, prove why does it. If not, explain why it does not.

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Q: the matrix A = and explain why or why not this matrix is diagonalizable

A: In the given question, concept of diagonalizable matrix is applied. Diagonalizable Matrix Any square…

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: [2 Given that; a=1, b=2, c=0, d=1 Explain why the matrix a b c d is not diagonalisable.

A: Here the given matrix Let x be tha eigen value of A matrix Then

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

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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: How do I know if I can invert a matrix or not? What is a square matrix?

A: Ans(i):

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :