a) A and B are 3x3 matrices with |2B| = 2 and [A| = -5. By using properties of %3D determinant or elementary operation, find i) [BJ. ii) [(2AT)²(A-!B²)-1|.

Q: Let A be an n × n nonzero matrix satisfying A10 = O. Explain why A must be singular. What properties…

A: Here given

Q: By computing the determinant of a suitable 2 x 2 matrix, find the area of the parallelogram with…

A: As we know that; The expression for the area of the parallelogram with adjacent sides a→ & b→;…

Q: The determinant of a 2 by 2 matrix A is equal to the area of the parallelogram with two adjacent…

A: Given the 2 by 2 matrix A. We have to find the determinant of a  matrix A is equal to the area of…

Q: Prove that a 3 by 3 determinant in which the entries in column 1 equal those in column 3 has the…

A: We know that the value of a determinant with any two identical rows or any two identical columns is…

Q: Compute the determinant using a cofactor expansion down the second column. 1 |-2 1 -6 -2 8

A:

Q: Consider a 20x20 invertible matrix A whose determinant is 2. Let B be the matrix obtained from A by…

A: Given- A is 20x20 invertible matrix whose determinant 2. Matrix B is obtained from A by…

Q: True or False If determinant of matrix A is equal to 1, then the adjoint of A pre-multiplied to A…

A: Identity matrix: A square matrix whose diagonal elements are all one and all the non-diagonal…

Q: . Prove that,if row 2 of a 3 by 3 determinant is multiplied by k,k ≠0, and the result is added to…

A: Explanation: Given that, 3×3 matrix  Suppose  A=abcdefghi Find the determinant of A…

Q: d. Using Matrix [B1] and [B2] prove that by solving the determinant of these matrices separately and…

A: Note:- You mentioned letter "D" but don't mention it is sub part (d) or matrix (d). For matrix D…

Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

Q: Consider a 20x20 invertible matrix A whose determinant is 2. Let B be the matrix obtained from A by…

A:

Q: Can we use cofactor expansion in a 2 x 2 matrix? 2. What is the determinant of a 1x 1 matrix?

A:

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: 1.What is the definition of the cross product?2. How is the determinant of a 3 × 3 matrix used in…

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Q: If a 4 x 4 matrix A with rows v1, v2, V3, and v4 has determinant det A = 4, %3D 4v1 + 5v2 7v1 + 9v2…

A: See the detailed solution below.

Q: By computing the determinant of a suitable 2 x 2 matrix, find the area of the parallelogram with…

A:

Q: 2. Use determinants to calculate the area of the triangle with vertices (-1,2), (5,-3), and (4,4).

A:

Q: 2-compute the determinant of the matrix if 31 -1 A= 2 1 1 -2 4.

A: Given: A=-1032151-24

Q: [2 11 Find the determinant of matrix -1 0 3 by using 1 2 0 (a) cofactor expansion, (b) properties of…

A:

Q: Consider a 20x20 invertible matrix A whose determinant is 2. Let B be the matrix obtained from A by…

A: This question is from topic determinant of matrix.

Q: Find a 3 x 3 determinant equation similar to that in Exercise 7 that describes the equation of the…

A:

Q: Let and Compute the area of the parallelogram determined by four points with position vectors u, v,…

A: This question is from matrix

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

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

Q: Prove WITHOUT using the product property of determinants: If M, N are triangular matrices, |MN| =…

A:

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: Let and i = Compute the area of the parallelogram determined by four points with position vectors ū,…

A: We need to find area of parallelogram.

Q: 8) Write an augmented matrix that represents the system of equations, and use Cramer's rule to solve…

A: Consider the following system of linear equations: 2x+3y+z=43x-z=-3x-2y+2z=-5 Rewrite the system of…

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: If matrix B is obtained by multiplying matrix A one row or one column by a constant, then the…

A: Solution:-

Q: Find the determinant of a 10 x 10 matrix which has a 2 in each main diagonal entry and zeros…

A: Given matrix, 10 x 10 matrix which has a 2 in each main diagonal entry and zeros everywhere else.

Q: Refer to Matrix A and B, determine the following 6. co-factor of az21 and a33 of A? 7. determinant…

A:

Q: Let [(1a)] Compute the area of the parallelogram determined by four points with position vectors i,…

A: As we know that area of parallelogram is =Base ×Height

Q: [2 3 What is the determinant of the product of matrices A: and |3D 0 1 -17 B = 2 1 Artivat 2.

A:

Q: The volume of a parallelepiped having A, B and C as edges can be obtained by finding the determinant…

A:

Q: APPLY THE GAUSS ELIMINATION METHOD TO FIND THE DETERMINANT OF THE MATRIX.

A: Consider the given matrix. A=09-30-4-50755-20-103-700-1004-80-710 Now, use the gauss elimination…

Q: Find the determinant of given matrix using row reduction form (upper triangular form only). Then…

A:

Q: (1 point) If the determinant of a 5 x 5 matrix A is det(A) = 9, and the matrix B is obtained from A…

A:

Q: (a) Compute the determinant of the matrix by expanding along the second row (b) Compute a row…

A: We have: A=21-250146251-24215 Part (1) Finding the determinant of the matrix by expanding along the…

Q: matrix

A: Here given that matrix is 1 cross 1  let matrix is A=[a] where a is any number

Q: Compute the determinant of 1 1 2 3 A = -1 -1 0 -1 -2 3 by using row operations to obtain upper…

A: Given, A=12100123-20-1-1300-1

Q: Calculate the determinant of the n × n matrix

A:

Q: a.) Can we use cofactor expansion in a 2 x 2 matrix? b.) What is the determinant of a 1x 1 matrix?

A:

Q: If B is a non singular 2x2 matrix and k is a non zero scalar. What is the determinant of B

A:

Q: Using Laplace expansion, the 4x4 matrix will be reduced to 4 terms with a 3x3 minor determinant.…

A: Answer is mentioned below

Q: 6) Find the determinant of the matrix using the method of expansion by cofactors. -3 2 1 5 6 4 2 -3…

A: Answer is -75 Explanation is given below..

Q: Why is the determinant of the original matrix and the diagonalized matrix the same. Prove it.

A: Consider the provided question,

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

A:

Q: Suppose AB = AC, where B and C are nxp matrices and Ais invertible. Show that B= C. Is this true, in…

A: