In general, matrix multiplication is not commutative (i.e., AB = BA). However, in certain special cases the commutative property does hold. Show that (a) if D1 and D2 are n × n diagonal matrices, then D1D2 = D2D1. (b) if A is an n × n matrix and B = a0I + a1A + a2A2 +· · ·+akAk where a0, a1, . . . , ak are scalars, then AB = BA

Q: If A and B are similar, then there exists a matrix P such that Bk = P-1AKP. Use this fact to find…

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Q: Consider the two matrices: 4 -5 1 B = A = -6 -3 Compute A +3B. The result is equal to:

A: GivenA=24-60 B=1-5-32To compute12A+3B

Q: If A and B are 3 x 3 matrices, det(A) = 3, det(B) = -6, then det(AB) = det(2A) = %3D det(A") =…

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Q: Given the following matrices A and B, find a matrix C in M3.3 so that {A, B, C} is linearly…

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Q: For matrix A, (A^3) = 1, A^(-1) is equals to: * A^2

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Q: Suppose A is an n x n matrix and B is an invertible n x n matrix. Simplify the following: a) (BAB)?…

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Q: given that A is a m x n matrix and B is a n x k matrix, and that m > n and A is full rank, can we…

A: Please check step 2 for solution.

Q: Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

A: See the attachment

Q: Find the matrix product AB, if it is defined. -2 3 -2 0 A = B = 3 2 -1 1 O A. 4 0 O B. 1 3 -3 2 -8 2…

A: A = -2332B = -20-11

Q: If A and B are 5 x 8 matrices, and C is a 3 x 5 matrix, which of the following are defined?  A-C…

A: If A and B are 5 x 8 matrices, and C is a 3 x 5 matrix. Then, (1) A - C is not defined, because, A…

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: Find diagonal matrix for given matrix by using formula: D= CAC [1 A = lo -2 2 01 -21

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Q: Given two matrices: -- - [1 A = |2 2 1 ] -1 and B = [1 |0 1 lo 0 -28] 2 1 -3 [3 -2 -: -1] a) Check…

A: Given that: A = 12125-13-2-1 and B = 12101-300-28 To show: A is row equivalent to B we have to…

Q: If A is an n×n matrix with Col A​ =Rn​, how many solutions will there be to Ax​=b​, for any b in…

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Q: If A is a 3 x 3 matrix and B is a 2 x 2 matrix, then Select one: True False det(A) # det(B).

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Q: Select the pair of matrices, A and B , for which AB = 0, even though A + 0 and B 0. 6 4 1 -1 O A =…

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Q: Given the matrix      A=       [4 -1   0   2] , then the trace of A^3 is?

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Q: The matrix A5 x 3 may have a rank = 4 %3D Select one: O True O False

A: Answer:   False  As rank of a matrix is always less than or equal m or n if order of matrix is m x…

Q: Let A be a 3x3 matrix, and suppose that the matrix B is obtained from A by the following row…

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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: If A and B are n x n symmetric matrices, then AB is symmetric. ... (A) True B) False

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Q: If A and B are 8 x 2 matrices, and C is a 4 x 8 matrix, which of the following are defined? DA. BTCT…

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Q: If A is a 4 x 6 matrix and the dim Nul A​=3, what is dim Col A​?  Justify your answer.

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Q: If A and B are m × n matrices and C is an n × p matrix, then (A + B)C = AB + BC. TRUE OR FALSE

A: Here we define true false for matrix multiplication.

Q: Given a 3x3 matrix that det (A)=8 find the valueb) of c if in terms of a scabrcand A=12 3. 24 C-2 3…

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Q: Consider the matrices. -1 6. -4 -2 A = 4 2 -8 8 and B = 2 %3D -7 -11 6 5 What matrix results from B…

A: Solution-

Q: Are the two matrices similar? If so, find a matrix P such that B = P−1AP.

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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: If A and B are 4 X 4 matrices, det(A) = 1, det(B) = 4, then  det(AB) = ? det(3A) = ? det(AT) = ?…

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Q: Given that A is a 4 × 2 matrix and B is a 2 × 1 matrix, a. Is AB defined? If so, what is the order…

A: a) A is a 4 × 2 matrix and B is a 2 × 1 matrix Since number of coulmns of A=number of rows of BSo AB…

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

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Q: If A and B are 2 x 8 matrices, and C is a 7 ×2 matrix, which of the following are defined? A. AB В.…

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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: Are the two matrices similar? If so, find a matrix P such that 8 = PAP. (If not possible, enter…

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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: If A and B be 2 x 2 matrices, then (A + B)(A – B) = A² – B?. A True False

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Q: Given matrices a and B, if AB = 0, then either A = O or B = O. O True O False If A and B are…

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

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Q: Imagine you have matrices A, B, and C, which of the following is false? The transpose of a sum of…

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Q: If A is a 7 x 5 matrix and B is a 7 x 8 matrix, then (A) (BTA) is a 8 x 7 matrix (B) (B" A) is a 7 x…

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Q: If A and B are similar, then there exists a matrix P such that Bk = P-1AKP., Use this fact to find…

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Q: Find 2x2 matrices, A and B, such that AB = 0, but BA is NOT EQUAL to 0.

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

A: Given statment is true for all the matrix which satisfies the commutative property otherwise…

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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: Two nonzero 2 × 2 matrices A and B such that (A+B)² = A² + B².

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Q: If A and B are nxn matrices, then (AB)²=A²B²_ A) True B) False

A: Solution

Q: Given that A is a 1 x 7 matrix and B is a 5 x 1 matrix. (a) Is AB defined? If so, what is the order…

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Q: Given the matrices A= 1 −4 −1       4 3 −1      4 −4 −2 and B= −5                0…

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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.