I want to know about change of basis matrix and what does it mean by diagonalization of a matrix.

Q: What is Matrix trace?

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Q: Define bidiagonal matrix.

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Q: Explain the conditions, how to find a fundamental matrix for the system?

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Q: Determine if the matrix is diagonalizable

A: Given matrix, A=200-121101 we know that, if a matrix A is an n×n matrix, then it must have n…

Q: elementary

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Q: Find the basis of row space of the matrix A given in the attached image . Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1, R3⇒R3+2R1, R4⇒R4-2R1,…

Q: What is Orthoganal Matrix?

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Q: Which one of the matrices below is singular( Not invertible )?

A: A matrix whose determinant is zero is called as a singular matrix. Let us verify the options. (a)…

Q: Show that the product of two orthogonal matrices is also an orthogonal matrix. Is the product of two…

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Q: What is mean by Matrix? Define elements matrix?

A: Matrix:- A set of numbers arranged in rows and columns so as to form a rectangular array is called…

Q: Define Square matrix?

A: A matrix is the arrangement of data in rows and columns.

Q: matrix with eig satisfies

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Q: Explain the reason, why we factorize real matrix to get singular value decomposition ?

A: To Describe : Why do we factorize real Matrix to get singular value decomposition

Q: Define Triangular matrix ?

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Q: Under which conditions an inverse matrix be defined for a matrix?

A: There are two conditions for matrix to be invertible.

Q: What do you mean by Jacobian matrix ?

A: The Jacobian matrix for the system of differential equation is, dx1dt=f1x1,x2 and dx2dt=f2x1,x2

Q: State whether the matrix is diagonalizable or not. [::] diagonalizable O not diagonalizable

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Q: Can you please help me th

A: Given,              x1=011, x2=2-10, and x3= 10-2 be eigenvectors of A which corresponds to…

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: Define the term matrix equation.

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Q: why cant we just multiply the 1/det(A) with the transpose of matrix like indicated in the red…

A: I am attaching image so that you understand each and every step.

Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: What does linear independence mean with matrices in linear algebra? I don't understand the concept…

A: In this question, we have to give the definition of linear independence of matrices in linear…

Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

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: What is orthogonal and normal matrix? Can every orthogonal matrix be normal matrix and vice versa.

A: The commutative property of matrices can be stated as . The matrix obtained by interchanging the…

Q: How to make this matrix diagonally dominant?

A: A square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of…

Q: What is the multiplicative identity property? (applied to matrices and scalars)

A: Given: multiplicative identity property

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

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Q: Prove that the product of two upper triangular matrices is always another upper triangular matrix.

A: We have to prove that the product of two upper triangular matrices is always another upper…

Q: Could you explain the difference between finding the orthonormal basis of a matrix vs finding the…

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Q: Define matrix-vector multiplication.

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Q: Explain the mandatory conditions for the addition of two matrices?

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Q: find if the vector x is in the range for matrix A

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Q: Explain the term Gradient Matrix?

A: According to the question, we have to explain the term gradient matrix. The term gradient means the…

Q: Determine if the matrix is diagonalizable.

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Q: Can arrowhead matrix be similar to a tridiagonal matrix?

A: An arrowhead matrix is one that is a square matrix with zero entries everywhere except on the…

Q: Find change of basis matrix from ((1,2), (3,5)) to ((2,5), (3,7))

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Q: Is it true that Every identity matrix is a diagonal matrix? explain a reason?

A: A square matrix B=[bij] of order n is a diagonal matrix , if all its non-diagonal elements are 0,…

Q: Define Diagonal matrix.

A: Diagonal Matrix: A matrix having all the entries are zero except the diagonal entries is called the…

Q: What is the standard basis of a skew-symmetric matrix?

A: To give the standard basis of a skew-symmetric matrix.

Q: Explain the term Unitary Matrices.

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Q: What is a banded matrix and what are the types of these matrices?

A: See the attachment

Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal

Q: what is the Dim of a matrix, like if there is Matrix A, what is Dim(A)? Can i have example too?

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Q: What are the Symmetric Matrices?

A: we know that if transpose of a matrix is equal to itself, then that matrix is said to be symmetric…

Q: Define an orthogonal matrix.

A: A square matrix is an orthogonal matrix if its transpose is equal to its inverse matrix. Let A is a…

Q: Explain Identity Matrix?

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Q: Show that the product of two orthogonal matrices is orthogonal.

A: Note:  We are allowed to solve one question at a time so kindly upload rest of the questions as next…

Q: Find out two examples for each types of matrices and write down it's order also

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