Let A be an n x n matrix such that for all 1 <= i,j <=n, aij = 1 or aij = -1. Prove that the determinant of A is an integer divisible by 2n-1.

Q: Let t, ao,..., an-1 be real numbers. As usual, let Id, denote the n x n identity matrix. By using…

A: Given: tIdn-0   -a01⋱  -a1 ⋱⋱ ⋮  ⋱0-an-2   1-an-1 To find the determinant of the given matrix.

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: 100 110 0 121 :/つ

A: Please see the below pictures for detailed solution.

Q: Prove that for a diagonalisable square matrix A, the determinant is the product of the eigenvalues…

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Q: Let U be a square matrix such that UTU = I.  Prove that the determinant U = + 1.

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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: Use a determinant to decide whether the matrix is singular or nonsingular.

A: We know that a matrix is singular if and only if the determinant of A is zero.

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: Evaluate the determinant of the matrix A= [ w^3  w^4  w^2  w^6         0       w^3  w^5  w^3…

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Q: Prove that the determinant of the matrix 1 1 -1 X2 A=1 n-1 X3 Х3 хз n-l 2 1 Хn Xn п II (x-x) is…

A: To prove the determinantal identity

Q: Calculate the determinant of C. For what values of k is C invertible?

A: Given

Q: a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. b) Consider the…

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

Q: 1. Let A, B and C be n x n matrices such that det(A) = 4, det(B) = 3 and det(C) = -1. (c) same rows…

A: See the detailed solution below.

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

A: Given A is n×n b is a known n-dimensional vector and x be unknown vector defined by solution of Ax=b…

Q: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

A: Reduced matrix A in upper triangular matrix by using of row operation then find its determinant.

Q: Find the area of the triangle with vertices (1, 0), (2, 2), and (4, 3)

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Q: Compute the determinants of the follow- ing matrices. 3 2

A: The solution is given as follows :

Q: n x n matrix A is called skew-symmetric if AT = -A.  Show that is A is skew sy

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Q: Let A, B and C be n × n invertible matrices such that |A| = 2 , |B| = -3 and |A+ I| = 6. Find…

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

A: The given matrix is 321-1-23. Compute the determinant as follows.

Q: Use the cofactor expansion theorem to evaluate the given determinant along the specified row or…

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Q: Compute the determinants in using cofactor expansion along the first row and along the first column.

A: Consider a determinant: D=1-10-10101-1……1

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 matrix A, below, by using row operations to transform A to an…

A: This question is related to matrices.

Q: ) Let A be a nonsingular matrix, consider the 8. 2 matrices A- -6 4 10 1 (a) ( :) Find the…

A: See the answer below

Q: Find a concise 3 * 3 determinant formula that gives the area of a triangle in the xy-plane having…

A: To determine the determinant formula that gives the area of a triangle.

Q: Let A = [a1, a2, a3] be a 3 x 3 matrix whose columns are a1, a2, a3 and whose determinant is detA =…

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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 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: Prove that for an NxN-dimensional orthogonal matrix A a) the determinant |A| = ±1 b) the sum of the…

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Q: Use the concept of volume to explain why the determinant of a 3x3 matrix A is zero if and only if A…

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

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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: 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: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

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Q: Calculate the determinant of the n × n matrix

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Q: Compute the determinant of the given matrix. If the determinant is nonzero, use the formula for…

A: The solution are next step

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: Let A be an x n matrix and let det(A) denote its determinant. Then O the null space of A has…

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Q: By calculating AB and evaluating the determinants, verify that det AB = det A det B a12 b12 for the…

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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: 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: Expand the determinant of B by the second column and evaluate the occuring algebraic subdeterminants…

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

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Q: Use induction to prove that the determinant of a diagonal matrix is the product of all the entries…

A: Consider a diagonal matrix An, An=a10⋯00a2⋯0⋮⋮00⋯an Let Pn is is determinant of diagonal matrix An…

Q: 12. Use the properties of the determinant function to show that if A and B are any n × n matrices,…

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