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

Q: Can a matrix be similar to two different diagonal matrices? Explain.

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Q: What is the Skew-symmetric matrix?

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

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Q: Find the dimensions of the given matrix.

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Q: Give an example of a matrix M where MMT and MTM are not equal matrices.

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Q: why is the matrix like that?

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Q: Give an example of a 3 x 3 lower triangular matrix A that is not diagonal. A =

A: We write the 3x3 lower triangular matrix which is not diagonal

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

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

Q: What is the rank of the matrix?

A:

Q: What is the coordinate matrix of that describes the following quadrilateral ABCD?

A:

Q: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

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

A:

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: Due to what property, applied to the matrices and scalars below, do we know that (cd)A = c(dA)?

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Q: Explain why the matrix is not diagonalizable.

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Q: Explain the term symmetric matrix.

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Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: Reduce the matrix to echelon form and find its rank

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Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

A:

Q: An n x n matrix that is orthogonally diagonalizable must be symmetric.

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Q: Find the indicated Matrix, if possible. Show and explain your work. |ЗА +В

A: A=4-472B=-243-73A+B = 34-472+-243-7

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

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: Which matrix is not similar to

A: Given that Matrix- X= 011112-12114, A=21-121011114,B=01111411-122, C=0-111-12121-14, D=100030003,…

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: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

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

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

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Q: Why is working with orthogonal matrix computationally ecient?

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Q: Which one of the following matrix is a Lower triangular matrix?

A: A triangular matrix is a special kind of square matrix in linear algebra.    Find: Which one of the…

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

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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: If A is a symmetric matrix, does it follow that the transpose of matrix A is also symmetric?…

A:

Q: Explain why the matrix is not diagonalizable.

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Q: 6. What 2x 2 matrix rotates the plane clockwise by 90° while dilating it by a factor of 2?

A: We need to find such a 2×2 matrix which rotates the plane clockwise by 90° while dilating it by a…

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: Which of the following is a lower triangular matrix?

A: GIVEN - MATRICES ARE GIVEN TO FIND - LOWER TRIANGULAR MATRIX  CONCEPT - IN LOWER TRIANGULAR MATRIX…

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: Every matrix has a unique reduced echelon form. Is this true or false?

A: Given statement is “Every matrix has a unique reduced echelon form. Is this true or false?”

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: Find an LU factorization of the matrix A (with L unit lower triangular). 3 -4 -3 L = U = A,

A: The solution is given below

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

A:

Q: What is the coordinate matrix that describes the following quadrilateral ABCD?

A: given figure

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: What is the coordinate matrix that describes the following quadrila

A: Coordinate matrix denote the coordinate of quasrilateral ABCD

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.