Does Size of a product matrix in Matrix Multiplication matter? explain the suitable size?

Q: What are the three elementary matrix row operations?

A: What are the three elementary matrix row operations?

Q: In class, I hinted that normal multiplication (of numbers) is commutative and that matrix…

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Q: What is the Skew-symmetric matrix?

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Q: What is the closure property of multiplication? (applied to matrices and scalars)

A: Closure property of multiplication: (applied to matrices and scalars) Multiplication of any two…

Q: Determine whether the matrix is elementary. If it is, state the elementary row operation used to…

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Q: Define Square matrix?

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

Q: matrix question

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Q: Is it possible to find a matrix in row echelon form whose column (iv) space is the same as that of…

A: (iv) No , it is not possible to find a matrix in row echelon form whose column space is same as that…

Q: What is the rank of the matrix?

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Q: Does Matrix multiplication commutative and associative?

A: The matrix multiplication doesn’t generally follow commutative property. That is, for two matrices A…

Q: What is zero matrix, explain each entry of which is zero?

A: Given problem:- Explain Zero matrix

Q: Define Triangular matrix ?

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Q: What is the rank of the matrix?

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Q: Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD.…

A: Yes, Given Matrix is diagnolizable.

Q: Define the basic required conditions for matrix multiplication?

A: Let A be a matrix of order mxn and B be a matrix of order pxq.

Q: Explain the process of Matrix multiplication?

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

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

Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: Find an LU-factorization of the matrix.

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Q: What is the closure property of addition? (applied to matrices)

A: Closer property of addition  A+Bis a matrix of the same dimension as A and B Notice that the sum of…

Q: Explain the fact Every rank one matrix is one column times one row.

A: Every rank of a matrix is one column times one row is not accurately correct.

Q: 9. When can a square matrix be diagonalized? When can a square matrix be diagonalized orthogonally?

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Q: How do you know whether a matrix is invertible?

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Q: If A is a 4 × 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 ×…

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Q: What type of matrix is a linear combination of scalar ma- trices? Justify your answer.

A: Consider n scalar matrices with each matrix in k×k order: A1, A2, A3, ⋯, An Also, let b1, b2, b3, ⋯,…

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

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Q: Envision a 2 x 3 matrix.

A: Let A be the matrix with order 2×3, which represents 2 as number of rows and 3 as number of columns.

Q: Explain the rank of a matrix?

A: The rank of a matrix is defined as the maximum number of linearly independent column vectors in 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: Explain the Main diagonal within a matrix ?

A: The main diagonal within a matrix consists of those elements which lie on the diagonal that runs…

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

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

A: Ans(i):

Q: What are the main important conditions need to keep in mind while multiplying matrices?

A: Main important conditions kept in mind while multiplying matrices:

Q: Explain the process of determining a minor in a matrix?

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Q: Explain why the matrix is not diagonalizable.

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Q: Difference between Simple Matrix & Adjecent matrix?

A: A Simple Matrix is just an array of numbers that can broadly be classified to 3 types - Upper…

Q: What is the reduced row echelon form of a matrix?

A: A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the…

Q: If a 2 x 3 matrix is multiplied by a 2 x 3 matrix, which of the below choices show the dimensions of…

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Q: n layman's term describe how LU factorization of a nonsingular matrix B can be found using…

A: Doolittle Algorithm: It is always possible to factor a square matrix into a lower triangular matrix…

Q: Matrix multiplication is always commutative? justify it.

A: Matrix multiplication is not always commutative.

Q: Illustrate the Matrix Notation and Terminology by using suitable example?

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Q: What is the rank of a 7x9 matrix whose null space is five dimensional? rank A =

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Q: How do the dimensions of the null space and column space of a matrix relate to the number of lead…

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Q: how to find the cofactor of a 4x3 matrix

A: Solution

Q: Is the reduced echelon form of a matrix unique? Justify your conclusion.

A: The row reduced echelon form of a matrix is  unique .

Q: Give an example of a 3× 3 diagonal matrix.

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Q: Construct the adjacency matrix. Why is it a block-diagonal matrix?

A: This is always block diagonal matrix in case of bipartite graph.

Q: Can u give 10 matrix terminologies and its definition.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.