The following elementary matrix multiplications realize the row reduction of the matrix A: A → 1 0 1 0 0 0 1 0 0 ⠀⠀⠀⠀⠀ 1 E₁A → 0 1 0 E₂E₁A → 0 -5 0 E3E₂E₁A = 0 0 0 1 E₁ 1 0 0 1 0 A → 0 0 1 0 1 0 E₂ 1 0 0 0 0 -4 What is the determinant of the row echelon form of A? (The matrix R on the right.) det(R) = Using the determinant of Rand the way it was obtained from Al, compute: det(A) = E4 5 0 3 -4 0 -2 4

Q: (iv). Find det(A¯1) of the following matrix: 1 3 -1 2 1

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Q: What is the determinant of a matrix that has been row reduced? For example, calculate the…

A: Let the given matrix is                      A=a11a12a13⋯a1n0a22a23⋯a2n00a33⋯a3n⋮⋮⋮⋱⋮000⋯ann The…

Q: A = 060 4 1 2 20 04

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Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

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Q: Compute the determinant of the following matrix -() 1 а а? 1 b b2 1 c c? A =

A: To find the determinant of matrix A

Q: Find determinants of the following matrices (a) 30 4 23 2 05 -1 (b) 2-2 3 2 3 a 1 3 (c) a b 1 -32 4…

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Q: 1. Compute the determinants of the matrices: 1 0 0 -1 1 1 3 3 1 1 0 2 2 -1 -1 2 1 3 2 1 2 -3 -2 -1 2

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Q: The determinate of Matrix A is: * 3-2 A = [1 4 0.5] 2 3 O 16.5 O 1.5 O 11 Non

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Q: Consider the following system of linear equations: y + z = 2 + X 3x - 2y + z = 1 y - z = 2 Let A be…

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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 by row reduction to echelon form. 1 -1 -3 0 4 -3 32 2 0-5 5 -2 4 75 Use row…

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Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: 1.) Find the determinant of the matrix A 4200 71 01 1006 0301

A: The given problem is to find the determinant of the given matrix A of 4*4.

Q: The determinant of the matrix of B = [1 2 3 1 1 2 is: 2 0 0 B = -5 |B|= 4 |B|= 2 |B| = 8 |B|= 6

A: Given matrix B=123112200

Q: Use Gaussian elimination to determine the determinant of the matrix: 1 1 1 1 1 1 44 M = 1 -1 2 -2 -1…

A: To determine the determinant of the matrix  M  using Gaussian elimination, we need to perform row…

Q: Find the determinant of the matrix det (M) = M = -2 -2 0 0 0 0 -2 0 3 -3 2 0 -1 FONO

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Q: Exercise 7.4.1 Use row operations to calculate the following determinants: 12 1 2 (a) 1 2 1 23 2 -4…

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Q: Find the determinant of the matrix a a b a a a b a A = a baa bаа а by applying appropriate…

A: For a given matrix A, |A| is the determinant

Q: refer  to  image  below. Find  determinant  of  following  matrix.  Justify  your  answer  with…

A: Since all the entries of the given matrix above the main diagonal are zero, the given matrix is a…

Q: 1 2a and its cofactor matrix C = 2b -2 **Suppose the matrix A =| 2а 4 20 4 answer the following…

A: Explanation of the answer is as follows

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: [A]-and (8) [: and (C]- then find (A +(8]C]

A: see below the answer

Q: Find the determinant of the following matrix using elementary row operation [1 2 2 A= |1 10 2 4 4 Is…

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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: 2. The following matrices correspond to the augmented matrix of a linear system of equations. GIve…

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Q: Compute the determinant of the following matrix: A = 6 5 1 -2 4 3 1 –4 2 1 6 2 (Show all your work.)…

A: Introduction:  A square matrix that is not invertible is called singular or degenerate. A square…

Q: Compute the determinants of the matrices: 0 1 1 3 3 1 1 2 2 -1 -1 2 2 31 2 2-3-2

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Q: Using row reduction, evaluate the determinant of the following matrix: 2 -1 3 1 -1 1 1 0 -2 3 2 -1 5…

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