Matrix multiplication is not commutative. That is AB is not equal to BA. But there are exceptions. Which pair of matrices M1M1 and M2M2 commute. a. When they are both symmetric. A matrix is symmetric when it is equal to its transpose. b. When they have the form M1=S+STM1=S+ST and M2=S−STM2=S−ST where SS is any matrix. c. When they have the form M1=I+SM1=I+S and M2=I−SM2=I−S where SS is any matrix. d. When they are both orthogonal (aka orthonormal or unitary). A matrix is orthogonal when its transpose is equal to its inverse.  e. They never commute.

Q: For a nonsingular matrix A and a nonnegative integer p, show that (Ap)−1 = (A−1)p.

A: The objective is to show that AP-1=A-1P for a non singular matrix A and a non negative integer P

Q: Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix…

A: I assume you know what is an argument matrix and what is rank of matrix .

Q: If A = (3), B = -10 33(, ) and C= (G° - 13) determine the matrix X such that AXB = 71, where I is…

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Q: If a square matrix A is not invertible, then the columns of A could be either linearly independent…

A: We know that if a matrix is invertible then its column are linearly independent. Column A is…

Q: If B is a matrix obtained by multiplying each entry of some row of a 2 × 2 matrix A by the scalar k,…

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Q: Let A,B be 3*3 matrix such that, det(A)=4, det(B) =5, find det(2AB)= 100 Select one: O True False

A: Given  det(A) = 4 det(B) = 5

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: Let A be an m×n matrix and let B be an n×p matrix. Show that if the columns of B are linearly​…

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Q: If P is an n x n matrix with orthogonal columns, then PT = P-1 Select one: True False

A: Let P be the given orthogonal matrix

Q: If C is a matrix of 6 x 6 and the matrix equation C x = v is consistent for every v in R®, is it…

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Q: . Which matrix, when multiplying another matrix on the left, permutes rows two and three of the…

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Q: If a 3 by 3 matrix has det A = -1 , find det(½A) and det(-A) and det(A2) and det (A-1 ).

A: Properties of Determinant →i detcA=cn.detA    where n is the order of square matrix .ii det…

Q: If A is a square matrix, then Ker(A) = Ker(RREF). True or false?

A: If A is aquare matrix then we have to check Ker(A) =Ker(RREF(A))

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

A: Given: The linear system of equations is, The inverse of a matrix is calculated by using the…

Q: If A is an nxn invertible matrix, then det(A-1) is equal to O det (A)-"det(adj(A)) O None of these…

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Q: If C is a matrix of 6 x 6 and the matrix equation C x = v is consistent for every v in R°, is it…

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Q: Let A,B be 3*3 matrix such that , det(A)=4, det(B) =5, find det(2AB)= 100 Select one: O True False

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Q: Decide whether the matrix -7 1 4 A = -12 1 8 -10 1 7, is diagonalizable over R. If it is,…

A: -714-1218-1017

Q: Let A be a 3×3 matrix, and suppose that the matrix B is obtained from A by the following row…

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Q: Determine if the matrix A = -1 1 1 is diagonalizable. If so, find P, D, so that -3 -1 -3 DDD-1

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Q: Is the following matrix 'B' diagonalizable?

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Q: If B and C are all invertible n x n matrices, then BC-l is the inverse of BC. O True O False

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Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

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Q: If A is a m × n matrix and B is a n × p matrix then AB is a m × p matrix. True or False

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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 the matrix -3 4 3 A 3D 4 3. 1 12 and if 1 u = and V = 3.

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Q: Given the matrix G -K and de = Then do and d, are G - conjugate if d, is given by Non of these

A: We know that,  Two vectors u, v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0  (Here…

Q: Give an example of a matrix A such that (1) Ax=b has a solution for infinitely many b ∈ R3 but (2)…

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Q: Determine whether the given matrix A (3x3) is diagonalizable and, if it is, give a diagonal matrix…

A: Given :A=120020113We find the matrix P and a diagonal matrix D so that P-1AP=D.

Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

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Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: For the matrices 1 -3 1 -2 A = 4 and B 2 5 in M2.2, determine whether the given matrix is a linear…

A: The given Matrix is a Linear combination of A and B.

Q: Given two matrices X and Y which are d ×d and invertible, judge whether the following matrices are…

A: Answer and explanation is given below....

Q: If A and B are similar, then there exists a matrix P such that BK = P-AKP. Use this fact to find B,…

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Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

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Q: Suppose that A is a 3×3 matrix and det (A) = -4. What is det (4A)?

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Are the two matrices similar? If so, find a matrix P such that B = p-1AP. (If not possible 1 0 0 1 0…

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Q: If A and B are nXn matrices, then (AB)²=A²B? A True

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Q: If A is a square matrix, then A2 is defined. TRUE OR FALSE

A: For matrix multiplication to be defined, the number of columns in the first matrix must be equal to…

Q: Find Hhe uinuerse of the matrix (if it exis ts). (if an answer does not exist, enter DNE.) 1 -3 -1…

A: Note:-  We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: Find a pair of unequal 2 × 2 matrices A and B , other than those given in Example 9, such that AB =…

A: Let A=0-10  2  &  B=3500.

Q: Given the matrices Anxm, Bnxp, Cnx n ₁ Dm x p , E p : ‚ B₁ x p ₁ C ₁ x n , Dmxp , Ep xn and Cnxn is…

A: Note: Inverse of a singular matrix does not exists.

Q: If the RREF of All is I| B, then AB is the identity matrix. A) True B) False

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Q: If det (A) = 0, then two of the columns of A are the same, where A is an n × n matrix. True

A: False

Q: Use Gaussian Elimination to carry the following matrix to a REF: 1 -1 2 3 -2 2 -4 -5 1 -1 1 4 2 -2 3…

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Q: Compute the matrix (BA')', if it exists, when the following matrices are given. - 1 1 A = -1 0 B= 0…

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Q: Let A be a 3x3 matrix where A2=I3, then det(A) is 1 or -1. Select one: 1-True 2-False

A: To find- Let A be a 3×3 matrix where A2 = I3, then detA is 1 or -1. True False

Q: Suppose matrix A is m×n and B is n×p. Prove that if the columns of B are linearly dependent, then…

A: Let A be m by n matrix and B be a n by p matrix.

Q: ) If A is a square matrix such that some row of A² is a linear combination of the other rows of A²,…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.