Let A, B be 4 x 4 matrices. Find two matrices so that rank(A) = rank(B) = 2 and rank(AB) = 1. A = B =

Q: Let A, B, C be n x n matrices. Verify that (a) A is similar to A. (b) If A is similar to B and B is…

A: Given A, B, C be n × n matrices

Q: If A and B are n × n diagonal matrices, show that AB = BA.

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Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 A= 12 2 -0 12 8 4,

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Q: Show that if A and B are two n × n matrices with the same diagonalizing matrix X, then AB = BA.

A:

Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

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Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: If A and B are matrices 3 x 3 order with 12A| = -1 and |2B³| = 16, then calculate |A-1B"|.

A: Here, A and B both are of the order 3×3. So, A-1 and BT are of the order 3×3. Now, from the…

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B) Upload an image or PDF of…

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Q: - |A°| |B°| • |4°|

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Q: Let A and B be n × n matrices and let x ∈ Rn. How many scalar additions and multiplications are…

A: Let A and B be n × n matrices and let x ∈ Rn

Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10! The matrix C = A – 2B is invertible. %3D [5.

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Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: Let A and B be square matrices of order 2 such that |B| = 4 .What is ( AB) '

A: To see 2nd step

Q: Let A and B be matrices such that the product AB is defined. Show that if A has two identical rows,…

A: Let A = [aij] be an m×n matrix and B = [bij] be an n×l matrix. Let C = AB = [cij] be an m×l product…

Q: Find values for the variables so that the matrices are equal.

A:

Q: Compute the product AB by the definition of the product of matrices, where Ab, and Ab, are computed…

A: We have to find the  product of matrix

Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: Let A and B be two matrices innRREF , if they are row equivalent then A=B.

A:

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

Q: If A and B are n x n matrices, and vector v is in the image of both A and B, then i must be in the…

A: True or false.

Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

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Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: Let A be a square matrix and det(A) = 2. If B is the matrix that results when –7 times the - first…

A: Given that: det(A)=2

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

A: Given,

Q: Determine whether the given matrices are linearly independent.

A: Given: 1234,4321 Let  λ11234+λ24321=0λ1+4λ22λ1+3λ23λ1+2λ24λ1+λ2=0

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: Let A be a 4 x 4 matrix with |adj(A) = -8, then 2A.adj(2A) - (where 1, is 4 x 4 identity matrix)…

A: Given that: A is a 4x4 matrix.                       |adj(A)|=-8

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: Let A be an n ×n matrix and B= A + I, where / is the identity matrix, then it is possible for A and…

A:

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1] A…

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

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 6 -2 -4…

A:

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

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Q: .

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Q: Find two 2 × 2 matrices such that ∣A∣ + ∣B∣ = ∣A + B∣.

A:

Q: Find the LU factorization of the matrix A, where 3 -5 2 -2 A = -1 -6 1 -4 1 2 1 2. 2.

A: Given matrix is A=−23−5232−22−1−61−1−4121. We have to find the LU-factorization of the matrix A. By…

Q: Let A be an n xn matrix and B= A+I, where I is the identity matrix, then it is possible for A and B…

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Q: . We can add (or subtract) two matrices only if they have thesame .

A:

Q: let  A and  B be  square  matrices of order n  such that  Ax=Bx  and x belongs to Rn  then   find…

A: Ax = Bx implies  Ax - Bx = O So, (A - B)x = O where x belongs to Rn  So, x belongs to the null space…

Q: Let A, B, C be n × n matrices and assume that A is invertible. Solve the equation A(B + X) = C for…

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Q: Compute the product AB by the definition of the product of matrices, where Ab, and Abz are computed…

A:

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

A: