How do the dimensions of the null space and column space of a matrix relate to the number of lead and free variables in the reduced row echelon form of the matrix? Explain.

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

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Q: The reduced row echelon form of the matrix A is I3 . Describe all possible matrices A.

A: Consider the reduced row echelon form of a matrix A is I3. We need to determine all possible…

Q: (3) Show that the system of quaternions can be represented as a system of real matrices of size 4 x…

A: Let h, j, k denote the imaginary units of algebra of Quaternions. Then the typical quaternion is in…

Q: What are the three elementary matrix row operations?

A: What are the three elementary matrix row operations?

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

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Q: What is a matrix?

A: Definition :                           A rectangular array of m × n numbers ( real or…

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

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Q: What do we mean by the transpose of a matrix?

A: Matrix is a set of number which are arranged in form of rows and columns. They have elements in them…

Q: 1 2 0 1 2 3

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Q: why is the matrix like that?

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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: The nullspace of a 5 by 5 matrix contains only x = 0 when the matrix has ___ pivots. The column…

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Q: #16

A: Recall the following facts.

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: Explain row vector in a 1 x n matrix?

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

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

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Q: Determine the size of the matrix.

A: Size of matrix is (no of rows × not columns)

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: Explain why the matrix is not diagonalizable.

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Q: the null space, and the row space of the matrix A.

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Q: What is a Augmented Matrix?

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Q: Explain the term singular matrix.

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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: 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: 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: 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 why the row vectors of a 7 x 2 matrix form a linearly dependent set. (Assume all matrix…

A: Rank of the matrix is at most min(7,2) = 2 dimension of row space = rank of matrix

Q: Explain the rank of a n*n non-singular matrix?

A: Consider Use the property of rank which states

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

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Q: Is the sum of two invertible matrices invertible? Explain why or why not. Illustrate your conclusion…

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Q: Why is working with orthogonal matrix computationally ecient?

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Q: Give an example showing that the rank of the product of two matrices can be less than the rank of…

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Q: Explain why the matrix is not diagonalizable.

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Q: Suppose A is a 3x5 coefficient matrix of a homogeneous system and suppose that A has two pivots.…

A: Solution is given below

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

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Q: How do you determine the sensitivity for each non zero parameter in this leslie matrix model

A: To determine sensitivity of 2x2 matrix. Let, the 2x2 matrix be a b c d Here,  True positive…

Q: Find the column space of the 10 x 20 matrix A if the system Ax = b is solvable for every b. Justify…

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Q: Let A be a 7 x 4 matrix. (a) What is the maximum possible dimension of the row space of A? - (b) If…

A: Given matrix A is 7×4. a) what is maximum possible dimension of the row space of A? b) If the…

Q: Prove that the nonzero rows of a matrix in a row echelon form are linearly independent

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Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…

A: We solve given problem with the help of rank nullity theorem

Q: Explain why the row vectors of a 4 × 3 matrix form a linearly dependent set. (Assume all matrix…

A: Given: The Matrix is 4 * 3 matrix

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

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

Q: Either the row vectors or the column vectors of a square matrix are linearly independent. True False

A: Any row vectors or column vectors of a square are said to be linearly independent if…

Q: What is a row matrix?

A: A matrix having only one row is called a row matrix.For example

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

A: What is the row-echelon form of a matrix? What is a leading entry? Row echelon form of a matrix is…

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

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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: What is a column matrix?

A: Definition of column matrix – A vector which is represented with a list of number is called a column…

Q: Explain why the row vectors of a 9 x 6 matrix form a linearly dependent set. (Assume all matrix…

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Q: A matrix which is not a square matrix is called a .6 Matrix

A: 6)  A matrix which is not a square matrix is called a

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.