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 why. (b) What conclusions can you make, if any, about the rank and determinant of A?

Q: Consider the matrix [1 0 31 A = 5 0 7 0 9 0 (a) Show that A is invertible, and compute its inverse.…

A: (a) To find: The inverse of matrix  103507090 and show that the matrix is invertible. Formula used:…

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: (a) det(A-1) (b) det(5A)

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Q: If A is a 3rd order matrix with a determinant of 5, then det((2A)^-1)=?

A: Using, Determinant formula

Q: Consider a square matrix A having characteristic polynomial p(A) = (1 + 1) ^ 2 (A - 2)(^ – 3) ^ 2 a)…

A: Dimension of a matrix : Let A be a square matrix with n rows & n columns .So its dimension is…

Q: (a) Consider the matrix 4 0 4 7 -5 1 A = 3 -1 2 1 -6 0 (i) Compute the determinant of A. (ii) Using…

A: Consider the matrix: A=7-51400403-12201-60 (i). To compute the determinant of A (ii). To explain…

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 3 A = |1 1 4 1 8 1 (a) Show that A is invertible, and compute its inverse. (b)…

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Q: Find the determinant of the elementary matrix. (Assume k ≠ 0.)

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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: Find the determinant of the following matrix by cofactor expansion. [ 1 0 0 2     0 0 2 0     0 2…

A: topic - determinant

Q: 1. Determine whether or not the following matrices are invertible by calculating the determinant. -8…

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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: 3. (a) Find the determinant of the matrix A below. 1 0 -1 0 0 1 1 0 -1 A =

A: The determinant value of the matrix abcpqrmno is aqo-nr-bpo-mr+cpn-qm when expanded about the first…

Q: 4.- Using Sarrus's rule, obtain the determinant of the given matrix. 2 -1 3 [A]: -1 %3D 2

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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: 1 1 3 3 1 3 3 0 2 1 1 1 1 2 0 1 2 1 0 1 1 3 6 0 1 4 2 3 2 1 0 2 4 2 1

A: Using property 9 and  If we get a matrix B from a matrix A with Multiplying by c( non zero) to a…

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: 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: A is a 3 x 3 matrix with det(A) = -2. What is the determinant of A-1 AT? Here AT is the transpose of…

A: Given; AT = A So, A-1AT = A-1A = Identity Matrix

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: Find the determinant of the matrix by reducing A to a triangular matrix. A = -1 2 3 1 1 2 1

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Q: Evaluate the determinant of the given matrix by reducing the matrix to row-echelon form. [4 1 4 1 10…

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Q: Compute the determinant of 15 2 4 3 4 1 A = 0 03 4 0 7 4 7 (a) by using a cofactor expansion across…

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Q: the

A: We have to give the example according to the given information

Q: Find the determinant of the elementary matrix. (Assume k + 0.) 10 0 5k 1 0 0 0 1

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Q: Evaluate the determinant of the given matrix. det(A) = A² + 3x + 12 A²+ 3A - 10 x² + 3x + 2 A²+ 3A -…

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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: Let A and B be 4x4 matrices such that det(A) = 5 and det(B) = 3. Compute the determinant of…

A: Explanation of the answer is as follows

Q: In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the…

A: This given problem is related to linear algebra. Given: n × n matrix A. First, we have to find a…

Q: Calculate the determinant of the following matrix. Show your work! -3 0 - 31 3 2 - 3

A: We have to find

Q: assume that A and Bare n X n matrices with det A = 3 and det B = - 2. Find the indicated…

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

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Q: Given that "a" is some nonzero constant, which of the following matrices has a non-zero determinant?…

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Q: assume that A and Bare n X n matrices with det A = 3 and det B = - 2. Find the indicated…

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Q: assume that A and Bare n X n matrices with det A = 3 and det B = - 2. Find the indicated…

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Q: 2. Consider the following matrix: -2 1 3 A = 5 3 1 -2 -1 (a) Calculate the determinant of A. (b)…

A: The given matrix is: A=-2134531-2-1

Q: 1. For an n xn matrix A, find a formula to compute the determinant of dA in terms of det(A), where d…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The determinant of a scalar multiple of a matrix A is c'det(A) where n is the dimensio of matrix A…

A: When We multiply any matrix by any scalar then all elements are multiplied by the same scalar. When…

Q: Α = Α 2-2 3 3 1 2 1 3 -1

A: Determinant of a matrix using cofactor expansion along second row is as…

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: The determinant of the matrix [ ª11 a12 A a 21 a22 is given by : det(A) = |A| = a11ª12-a21@22

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Q: Let A, B, C, D, and I be n x n matrices. Use the definition or properties of a determinant to…

A: According to the given information, Let A,B,C,D and I be n × n matrices . It is required to use the…

Q: Find the determinant of the elementary matrix. (Assume k ≠ 0.)

A: Given:  A=001010100 for finding determinants of given matrix we expand it along row first

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: Find the determinant of the elementary matrix. (Assumek + 0.) 1 0 0 6k 1 0 0 0 1

A: Here is the solution:

Q: Explain why the statement is true, or give a counter-example: If we know that A is a square matrix…

A: Given that A is any square matrix and A=QR be its decomposition.

Q: [1]a- Prove that a square matrix A is invertible iff A"A is invertible . b- Prove that without…

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