Let A and B be square matrices of order 6 such that det(A) = 4 and det(B) = 15. Compute the following determinants: (a) det(AB). (b) det(Aª). (c) det(12B)

Q: ) Compute the determinant of the matrix 10 2 3 -2 104 A 3D 0 130 1 2 4 1

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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: For the given matrix: 2 -1 2 -1 0 -1 0 -1 2 -1 a) Compute the determinant. b) Calculate the rank.

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Q: Evaluate the determinant of the given matrix by cofactor expansion along the indicated row.

A: The determinant of the matrix along Row 4, 021310-223-101-1120=a41C41+a42C42+a42C43+a44C44 From the…

Q: If the determinant of a 5 x 5 matrix A is det (A) = 8, and the matrix B is obtained from A by…

A: I am attaching image so that you understand each and every step.

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

A: Using, Determinant formula

Q: Find the determinant of the matrix below: 1 0 4 -61 |-1 2 3 5 2 5 0 3 2 1 -2 3J

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Q: Let A and B be 6 x 6 matrices, with det A = -10 and det B = 5. Use properties of determinants to…

A: Given that det A=-10 and det B=5 find a) det(3A) b)det(ATB-1)

Q: 12 1 14 2. 13 8 11 16 10 15 4.

A: To find the determinant of the given matrix

Q: -5 1 0 1 -6 0 5 2 0 A = 1 0 3 -1 0 1 0 -5 1 -6 6 -2 0 2 5

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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: Compute the determinant of the matrix using the best possible method. Zmatrix ((2 -2 6 4)(2 3 7 1)(6…

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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: For square matrix A, if its first row equals 5 times the third row, then its determinant is 0. True…

A: We are given with the matrix who is first row is five times the third row and we have to find the…

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

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

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: Use the method demonstrated in Example 5 to find the determinant of the matrix. 3 9 -6 0 -7 4 9 1 8.

A: Topic  = Matrix

Q: Find the determinant of the matrix, if it exists.  [2 5]

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Q: 0 9 -3 0 -4 -5 0 7 5 -2 0 -10 3 -7 0 0 -10 0 4 -8 0 -7 1

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Q: If the determinant of a 5 x 5 matrix A is det(A) = 7, and the matrix B is obtained from A by…

A: This is a Linear Algebra problem.

Q: Consider the following matrix  [ 0  -3  -2 ] [ 2   0    5 ] [ 0  -3   0 ] find its determinant

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Q: If the determinant of a 4 x 4 matrix A is det(A) = 7, and the matrix D is obtained from A by adding…

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Q: Q1): Prove that: A square matrix B has inverse if and only determinant of B is not equal zero.

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Q: A, B,C are 3 x 3 matrices with det(A) = -5, det(B) = 2, det(C) = 10. choose the option which is…

A: To find the determinant of AB2C-1, we use the following properties of the determinant for m×m…

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: Evaluate the determinant of the given matrix by cofactor expansion along the indicated row.

A: the given matrix is: 102015-130 we have to evaluate the determinant of the given matrix by cofactor…

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

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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: If the determinant of a 5 x 5 matrix A is det(A) = 9, and the matrix B is obtained from A by…

A: If A is n×n matrix then det(aA)= andet(A). Just use this property of determinant of a matrix and…

Q: Find the determinant of the n X n matrix A with 3's on the diagonal, 1's above the diagonal, and 0's…

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Q: 1 3 4 -2 3. 2. 3. 3.

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

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Q: If A is a diagonal matrix, its determinant is the product of its diagonal entries, and its inverse…

A: Given, a) Diagonal matrix,A=400000200000100000120000014 b) Diagonal…

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: 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: Compute the determinant of the matrix by cofactor expansion. T-4 3 -3 2] 0 -1 0 3 0 0 0 -3 1 4] 2 -2…

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Q: [1 2 -1] 1. If A = 3 2 4, verify that detA = detA". L1 3

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Q: If the determinant of a 3 x 3 matrix A is det(A) = 2, and the matrix B is obtained from A by…

A: Given any matrix A , then Bis the matrix obtained by multiplying any row(or column) of matrix A by k…

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

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Q: (b) Given that A and B are 3x3 matrices where det(A) = -3 and det(B) = 3. Compute the following…

A: solution:Given A and B are 3×3 matrices .Also, det(A)=-3 and det (B)=3.WE need to find detA2T.(2B)-1…

Q: Compute the determinant of the matrix 2 1 0 0 0 1 1 0 0 1 1

A: Given Matrix λ1000λ1000λ1001λ Its determinant λ1000λ1000λ1001λ