Explain the concept of Multiplication of a matrix by a scalar. Give an example.

Q: Diagonalize the matrix A 2 -2 if possible. 2 -3

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

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Q: Define matrix notation and terminology?

A: Matrix notation and terminology.

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: Explain Scalar multiplication of matrices?

A: We know that the term scalar multiplication means  the product of a real number and a matrix. In…

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: Is every diagonal matrix a scalar matrix? Explain.

A: We have to explain that every diagonal matrix a scalar matrix. We know that diagonal matrices are…

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

A: Given problem:- Explain Zero matrix

Q: Does the matrix have an inverse? Explain why why not. or

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Q: I cant understand what's going on. can this be explained with matrices?

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Q: Explain Column matrix along with an example.

A: A column matrix is a list of elements which is written in a column. It can also be called as a…

Q: Why is it important that the matrix is invertible? Give and example.

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Q: Define the term matrix equation.

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

A: To state: the associative property of multiplication (applied to matrices and scalars)

Q: What do you mean by transpose of a matrix? Explain their properties?

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Q: For Exercise, determine whether the statement is true or false. If a statement is false, explain…

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Q: Give an example of two matrices A and B such that BA exists, but AB is undefined. Explain why your…

A: Finding the product of two matrices is only possible when the inner dimensions are the same, meaning…

Q: What is the multiplicative identity matrix?

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

Q: product of a matrix and its inverse is

A: Matrix: Let A be a matrix  B is the inverse of the matrix. A=B-1 AB=I

Q: Define the matrix square root?

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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: Find the inverse matrix of A

A: We are given :A=13-201-6001 ⇒A=1(1-0)-3(0-0)-2(0-0)=1≠0 ⇒A is Invertible. Formula for Finding A-1:…

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: Explain how to find the multiplicative inverse for a 2 * 2 invertible matrix.

A: To find the multiplicative inverse of 2*2 invertible matrix.

Q: Use (ii) of the rank of a matrix by row reduction theorem to find the rank of the given matrix. (?…

A: The given matrix is 7-113.

Q: Define Scalar multiplication of matrices?

A: A scalar multiplication of a matrix is defined as the multiplication of that scalar value in all…

Q: Describe The Exponential of a Matrix.

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Q: What is Rank? Please describe. mxn The largest rank of a dimensional matrix can take what would be…

A: We have to define the rank of the matrix. Definition of rank:- The maximum number of its linearly…

Q: define: scalar multiplication (applied to matrices)

A: The term scalar multiplication is the product of a real number and a matrix.

Q: Give an example of a real square matrix that does not have an LU decomposition. Explain carefully…

A: Please see the below picture for detailed solution.

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

A: Given: multiplicative identity property

Q: Explain the general formula for the inverse of a matrix?

A: Given, Explain the general formula for the inverse of a matrix?

Q: Define the term Scalar multiplication of matrices?

A: Concept: A rectangular array of numbers (or other mathematical objects) for those the operations…

Q: Explain an example how to calculate matrix-vector multiplication.

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Q: make the matrix diagonally dominant

A: Diagonally dominant matrix: These are the matrix in which the absolute value of the diagonal element…

Q: Is every scalar matrix nonsingular? Explain.

A: Query- Is every scalar matrix nonsingular? Explain. Answer-  A non-singular matrix is a square one…

Q: Consider the matrix

A: Given, the matrix                    A=1-101-1121-141-10-112-2042-282-2

Q: Define concept of Matrices?

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

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Q: Explain Identity Matrix?

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Q: Determine whether the matrix B = is awesome or not. %3D

A: 7.1 To determine whether the matrix B is awesome or not. Where  B=i2−3232−i2and B is awesome if…

Q: Describe when the multiplication of two matrices is not defined.

A: Given, multiplication of two matrices

Q: Find values for the variables so that the matrices are equal. image 1 =image 2

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Q: Orthogonally diagonalize the matrix 1 -1 -2 A -1 2 -2 3

A: Given:   A = 1-1-2 -120 -203

Q: What is an Inverse matrix?

A: Inverse matrix: If A is a square matrix of order m, and if there exists another square matrix B of…

Q: Give an example of a nonzero 3 x 3 diagonal matrix A. A =

A: Diagonal Matrix: In linear algebra, a diagonal matrix is a matrix in which the entries outside the…

Q: What is the procedure for obtaining the inverse of a matrix?

A: Given:    Procedure of Inverse Matrix

Q: state the inverse of matrix attached

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Q: Find the inverse of the elementary matrix.

A: Given matrix, A=0110

Q: Define the properties of the inverse of a matrix?

A: