Express the matrix I 0] A = 5 3 and its inverse as a product of two elementary matrices.

Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

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Q: Find an SVD of the matrix. -7 3 A = - 3 - 1 O (Type an exact answer, using radicals as needed.) A =

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Q: Let A be the matrix Compute A50

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Q: Find an LUfactorization of the given matrix.

A: Given, To find LU factorization of the given matrix.

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Factorize the matrix into LU decomposition. [0 5 41 A = 5 1 2 1 2 3.

A:

Q: The multiplicative identity matrix of order 3 is I3 =_______.

A: Let the Identity matrix be…

Q: If the Reduced echelon form of A-λI is the identity matrix then what is the eigenspace (Eλ)?

A: We need to find the eigenspace (Eλ) if the Reduced echelon form of A-λI is the identity matrix. Note…

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: ) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s) for…

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Q: Find the inverse of the matrix using Gauss Jordan method?

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Q: VýB × VA

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Q: Write down the necessary conditions for the matrix B2*2 (2 ∗ 2 matrix) to have an inverse matrix.

A: Necessary conditions for a 2*2 matrix to have an inverse matrix.

Q: [1 2 2 3 1 0 1 1 4 4

A: Given matrix is  123101144find LU factorization of a given matrix

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: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

A: The change of basis matrix C from B2 to B1( or from the basis B2 to the basis B1 ): β1=-142,231  and…

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: 3. Is the trace of the product of two square matrices equal to the product of these two matrices'…

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Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: Which is the matrix inverse to the matrix 2 3 1 3 2 1 1 0 1

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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 x such that the matrix is singular. A- -2

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Q: Show that the matrix; is singular

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Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

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

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

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

A:

Q: Find a QR-decomposition of the matrix -1 1 1 -1 0 1

A: Here,             . Now, we will be finding the QR decomposition of the above matrix A.

Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Find x such that the matrix is singular.

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Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

Q: 3 (i);- 2

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Q: The multiplicative identity matrix of order 2 is I2 =_______.

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Q: Express the matrix and its inverse as products of elementary matrices. 10-2 A 0 5 4 0 0

A: NOTE: Refresh your page if you can't see any equations. .

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: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: Find the inverse of the matrix and verify that A-!A = AA1- 1. 4--10 A 3D 2. 8. A-1 Show My Work…

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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: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: Find two different 2 x 2 matrices A such that 1 0 A? =

A: Given: A2=1001

Q: APPLY A SERIES OF ROW OPERATIONS ONTO THE GIVEN MATRIX "A" TO FIND ITS INVERSE. [ A|1] => [ I|…

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Q: V3 Express 1 as a product of elementary matrices.

A: Solve by matrices

Q: Find the LU decomposition of the matrix 1 -3 1 7 -24 -8 2 -1 28

A: The given matrix is 172-3-24-11-828. Find the LU decomposition of the given matrix.   In linear…