Let A is an orthogonal matrix, that is, AAT = I and B? = I. Compute the determinanm of the matrix AB.

Q: Use the fact that ∣cA∣ = cn∣A∣ to evaluate the determinant of the n × n matrix.

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Q: Compute the determinant of A by by transforming the matrix into a triangular matrix. A = 3. -1 -3 4…

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Q: Let M be a 10 × 10 real matrix such that M2 = M and the determinant of the matrix cannot be 1. Does…

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Q: Consider a 4 x 4 matrix A with rows vi, v2, v3, and v4. If det(A) = 2, find the determinant of the…

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Q: Let A be an n x n matrix such that A3 = In. (a) Is A invertible? If so, what is A-1? If not, explain…

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Q: Let A 2x2 matrix. A satisfies with tr (A² ) = 5 and tr ( A) = 3. Find determinant of A.

A: Use property of eigen value

Q: Find the determinant of the matrix, if it exists.

A: Find out the determinant of the matrix. determinant for 2×2 matrix A=abcd  A=ad-bc So given matrix…

Q: -1 2 4 1 2 4 3 14 2 N N M 4 2.

A: Given that, 1-1243124-11322142

Q: Find the determinant of the following matrices:

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Q: Let A be 5x5 matrix. Which of the following criteria will ensure that A is diagonalizable over real…

A: Given A is a 5x5 matrix. We want to find criteria which ensure that A is diagonalizable.

Q: Let A and B be n × n matrices and let C = AB. Use determinants to show that if either A or B is…

A: Given :-  A and B  be n x n matrices  and  C = AB Singular matrices :-  A matrices singular when…

Q: Evaluate the determinant of matrix det(A), where 1 1 1 ... X2 T3 In ... A = ... n-1 „n-1

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Q: Consider the matrix 0 1 0 1 2001 A = 0 1 1 0 0 1 0 1, (a) By hand, compute the determinant of A. (b)…

A: The given matrix is                   A=0101200101100101 To find : (a) det A              (b)…

Q: If A is a n x n matrix with NON zero determinant, then its columns are a basis for a n dimensional…

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Calculate the determinant of the cofactor matrix of Matrix D.

A: To compute the determinant of the cofactor matrix of Matrix D.

Q: Linear algebra

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Q: -1 1 2 1 2 3 1 2 3 -1 2 3

A: Given lower triangular matrix :100⋯0120⋯0123⋯0123⋱0123⋯n

Q: if the given matrix is nonsingular, find its inverse. If the matrix is singular, verify that its…

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Q: Given the following matrices, find the determinant using МЕТНOD OF СOFАСTORS. -2 3 -1 A = -5 4 B = |…

A: Formula: Let A be n×n matrix with entries aij. For any i=1, 2, …, n the determinant of a matrix A is…

Q: If P is an invertible n × n matrix, show that: det(P−1A2P) = (det A)2 using the determinant…

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Q: Suppose that A and B are n x n matrices, where B is nonsingular. Prove that the determinant of BAB-¹…

A: We use properties of determinant.

Q: Compute the determinant of the matrix -1 2) 0 0 3 1 -1 -1 1 and find its inverse if it is…

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Q: Compute the determinant of the following elementary matrix 0 1 0 100 0 0 1

A: We use the expansion of the determinant along its rows to find the determinant of the given…

Q: Consider a 4 x 4 matrix A with rows vi, v2, v3, and v4. If det(A) = 5, find the determinant of the…

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Q: 2. If A is a 3 x 3 matrix, prove that the determinant of A is equal to the determinant of AT.

A: 2. Given A is a 3×3 matrix we need to show that determinant of A is equal to AT. Let A=abcdefghi.…

Q: Compute the determinant of the tollowing matrix using a cofactor expansion acro 56 -6 4 0 6

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Q: Suppose that a 4 x 4 matrix A with rows v1, v2, v3, and v4 has determinant det A = 2. Find the…

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Q: Consider a 2x2-dimensional matrix A for which A² = -A. a) What are all possible values of the…

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Q: Consider the following matrices: 1 0 1 4 3 1 1 2 -- %3D B = 0 1 1. [1 0 C = 0 1 -1 a) Find BC. b)…

A: If determinant of a matrix is non zero then it is invertible. Two matrix will add or subtract only…

Q: Consider a non-singular 2 x 2 square matrix M. If trace (M) = 7 and trace(M²) = 10, then %3D %3D…

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Q: Consider the NxN-dimensional matrices A and B, where B=S¹AS (with S an NXN-dimensional non- singular…

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Q: Determine whether the following matrix is invertible by finding its determinant. 4 -14 -56

A: Consider the matrix 14-14-56

Q: Let M be a 10 x 10 real matrix such that M² = M and the determinant of the matrix cannot be 1. Does…

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Q: Write down a n × n matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.

A: claim- write down a n×n matrix A such that CondA=1, but detA→0 as n→∞. it is known that condition…

Q: Calculate the determinant of the n × n matrix

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Q: The matrix of cofactors of A is precisely [adj (A)]T. O True False

A: I have given the answer in the next step. Hope you understand that

Q: ): Consider the 3 x 3 matrix -- -1 A = 3 -X where x is an unknown scalar. -1 Find the unknow x if it…

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Q: Consider matrix A E R33, such that det(A) = 3. Find determinant of matrix B = A-1. (2 · I) · A4.

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Q: = 1. Find the Suppose that a 4 x 4 matrix A with rows v1, V2, V3, and v4 has determinant det A…

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Q: Consider the Matrix  B = 0 1 2 1 2 −5 6 −4 3 Calculate the determinant det(B)

A: Given that, B=01212-56-43

Q: Let A be a known n x n matrix, b be a known n-dimensional vector and z be an unknown vector defined…

A: You asked to solve only (a). (a) Solution:  We will explain here how to compute the determinant of…

Q: 2. For the matrix A given in #1, compute the determinant using LU factorization.

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Q: Compute the determinant of the following matrix, without using a computing devise: 0 1 0 1 02 -1 -1…

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Q: Let A= (aj) and B = (b;) be the square matrices of order 3 such that bj = 3i+j aj for 1si,j< 3. If…

A: The given question can be solved as shown in step2.

Q: E. Compute for the determinant of the 4x4 matrix below using minors and cofactors. 3 2 2 2 2 1 1 1…

A: Given that: 0322020020110104

Q: Write down anxn matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.

A: claim- write down a n×n matrix A such that CondA =1 but determinantA→0 as n→∞ let the matrix be…

Q: ). If A is a 3 × 3 matrix with determinant 1, then 2A has leterminant 6.

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Q: Consider the following matrix 3 1 -2 A = -1 1 1 a) By evaluating the determinant of A determine in…

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