Let A be an nxn matrix, and let B be the matrix that results when the rows of A are written in reverse order. State a theorem that describes how det(A) and det(B) are related. det(B) = (– 1) 21 det(A) O det(B) = (1) W21 det(A) O det(B) = (– 1)det(A) O det(B) = (1) det(A)

Q: Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each…

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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 two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B)

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Q: If A is a 3x3 matrix and det(A) = 7, what is det(2A)?

A: Solution :-  Given : A is a 3×3 matrix               And det(A) =7

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: Compute AB, det(A), det(B), det(AB), and det(A + B) for the following matrices. 1 0 -1 4 0 5 0 1 A =…

A: Given that :- A=50113-1101 , B=10-1401010 find AB,detA,detB,detAB,detA+B

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

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A: we have solved this question by using an example.

Q: Suppose A and B are invertible 1 x n matrices. Check all the true statements below. ABB÷¹A = AI„ A =…

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Q: Let A and B be 4 x 4 matrices such that and det (B) = 5. det (A) = -3 Find the following. • det (BT)…

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Q: [3] 37 Let A = Write 2A. Is det(2A) equal to 2det(A)?

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

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Q: Express the matrix A = as the product of elementary matrices. 1 2 2 10 2 31

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Q: This is a linear algebra problem pretaining to matrix. Please find the cofactor C11(A), C12(A),…

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Q: Suppose that B is a square matrix with det(B) = -2. Find each of the following. (a) det(B6) = (b)…

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Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

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Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Compute AB, det(A), det(B), det(AB), and det(A + B) for the following matrices. A = AB = det(A) det…

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Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

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Q: 5. (16 points) Let A = [13¹], B = [-1¹ 63], and C = [29]. Compute each matrix sum or product if it…

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Q: If A is any square matrix. Then det(A) = a) det(A-1) b) det(AT) c) – det(AT) d) 0

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Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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