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

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: TRUE/FALSE The product of two elementary matrices is an elementary matrix.

A: False.  For example , the matrices are elementary matrices as they are obtained from I2 by single…

Q: Determine whether the given matrix is diagonalizable 3 1 A = 0 1 3

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Under what conditions will the diagonal matrix be invertible? Assume that A is invertible and find…

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Q: Explain why the matrix A + C does not exist.

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Q: Find an LUfactorization of the given matrix.

A: To Determine: find an LU factorization of the given matrix  Given: we have a matrix12-3-1…

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: The 2 ´ 2 identity matrix is:

A: To find:

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

A: Let the Identity matrix be…

Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

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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: Assume the invertible matrix A satisfies 10 4 1 1 A 6 A 1 A 1 3 4 -1 -1 -1 1 1 5 -2 1 1 3 4 -3 -1 1…

A: Detailed explanation mentioned below

Q: Find two different 2 × 2 matrices A such that

A: Given:               A2=1001

Q: Let A be a matrix 4 0 0 0 0 4 0 0 0 0 2 0 1 0 0 2 Determine if A is diagonalizable, and if…

A: Solving the above matrix problem using row operations

Q: 2 0 -1 2 0 0 1 1

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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: The multiplicative identity matrix of order 3 is I =

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Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

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

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Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: Show that the matrix is not diagonalizable.

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Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: Show that the matrix; is singular

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

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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: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

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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: Determine whether the matrix is orthogonally diagonalizable.

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Q: Show that the matrix is not diagonalizable.

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Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

Q: If A and B are orthogonal nxn matrices, then AB-1 is an orthogonal matrix. True False

A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

Q: Determine whether the matrix is symmetric.

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Q: Let A and B be n x n matrices.  Suppose that AB = On where On is a zero matrix of size n x n, and A…

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

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Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: 1. Show that matrix A is singular [1 2 0 A= 3 -1 2 -2 3 -2

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

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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: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: True False

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Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

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Q: Determine the dimension of the matrix. 17 15 0 50 3 3 0 1 6 7

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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: Is it true that the sum of invertible n x n matrices is invertible?

A: Given: The statement is : Is it true that the sum of invertible n x n matrices is invertible? It is…

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

A: Solve by matrices