Show that when performing LU decomposition of an nxn element matrix for a set of linear equations, there are n equations for n variables.

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: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). How many least squares…

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Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

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: | 1 2 -1 4 | | 3 3 5 0 | | 2 1 1 3 | | 4 2 2 1 |

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Q: Construct a matrix whose column space contains (1, 1, 1) and whose nullspace is the line of…

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Q: Show that the product of two 2 × 2 skew symmetric ma- trices is diagonal. Is this true for n × n…

A: The objective is to show that the product of 2×2 skew symmetric matrix is diagonal and also to…

Q: f A is 3×3 nonsingular matrix such that AAT=ATA and B=A-1AT then BBT=

A: Given that: A is 3x3 non singular matrix and AAT=ATA and B=A-1AT

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Find two 2 × 2 singular matrices whose sum is nonsingular.

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Q: A matrix that has the same number of rows as columns is called a/an________ matrix.

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Q: 2 -3 -2 3 1 2 -2 -1 3 3 [ 3 2 -2

A: The given matrix is  A=  2-3-2   3  1   2-2   0-1   3   3   2   3   2   2-2

Q: Find an LU-factorization of the matrix.

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Q: Consider the matrix

A: Given, the matrix                A=0-3-1020233 And the eigenvalues of A are λ=1, and λ=2.

Q: Determine the size of the matrix.

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Q: Find an LU-factorization of the matrix.

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Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

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: Factorize the matrix into LU decomposition. A=[ 054 512 123 Note; With complete solution

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Q: Consider a 3 x 4 matrix A in reduced row echelon form. What can you say about the image of A?…

A: We have say about the subspace Ab where b from R4

Q: ГО 5 4 5 1 2 2 3] A = [1

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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: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: Can we use cofactor expansion in a 2x2 matrix?

A: Can we use cofactor expansion in a 2x2 matrix?

Q: Is there any 2x2 matrix with all non-zero entries, that is not diagonalizable but invertible? If…

A: Solution

Q: What is trace of matrix (2A+3B)

A: Find the trace of the matrix(2A+3B)

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: Suppose A is the 3x3 zero matrix (with all zero entries). Describe the solution set of the equation…

A: We can explain the answer as below

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

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Q: Find an upper triangular matrix that satisfies 18 -8 0

A: Given  A3 = 1180-8 It is an upper triangular matrix , hence its diagonal are the eigen values of the…

Q: Write a 4  6 matrix with distinct non-positive entries and find its transpose.

A: The objective is to write a 4×6 matrix with distinct non-positive entries and find its transpose .

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

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Q: What is the transpose of matrix M=(-1,0,2)(0,-3,1)?

A: A matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.” We…

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: If a 6 x 6 matrix contains 19 zeros, show that there are 4 zeros which are all in distinct rows and…

A: A 6x6 matrix has 36 entries. Given if a 6x6 matrix contains 19 zeros, then to show that there are 4…

Q: Determine the size of the matrix. 2 -1

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Q: Find an LU factorization for the matrix: 1 2 1 2 1 2 -2 0 1

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Q: Find the number of 3x4 matrices in row echelon form, with entires from F = Z/2Z

A: To find the number of 3x4 matrices in row echelon form, with entries from F = Z/2Z.

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

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Q: Find the LU composition of 1 | - matrix 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: Find two 2 × 2 singular matrices whose sum is nonsin- gular.

A: We have to find two 2×2 singular matrices whose sum is non-singular. We know that when determinant…

Q: Must an upper triangular matrix be in row-reduced form?

A: A square matrix whose all elements below the main diagonal are zero,  is called an upper…

Q: Find a 3 x 3 orthogonal matrix P whose first two rows are multiples of (а) (1,2,3) and (0, -2,3),…

A: To find the matrix

Q: The i-th column vector of an AB matrix product can be calculated by multiplying A by the i-th B…

A: True Because take A=a11a12a21a22 and B=b11b12b21b22 Then the product of AB is,…

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

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Q: of the matrix

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Q: Find a sequence of elementary matrices whose product is the nonsingular matrix below.

A: Given non-singular matrix is :                                                          2-410   To…