Purchase Solution

Determinants and Adjugate : Proof

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

---
1. Write a proof for the following statement: If A is any n x n non-singular matrix, then det(adj(A))=(det(A))^(n-1). Show work.

Help:

det: is the determinant
adj: is the adjugate (or classical adjoint)

Attachments
Purchase this Solution
Solution Summary

A proof is provided linking the adjoint to the the determinant.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

1. Write a proof for the following statement: If A is any n x n non-singular matrix, then det(adj(A))=(det(A))^(n-1). Show ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Determinants and Cramer's Rule : Row Operations and Effect on Determinant, Computing Determinants and Solving Systems of Equations

    52110 Determinants and Cramer's Rule : Row Operations and Effect on Determinant, Computing Determinants and Solving Systems of Equations 1.

  • Proof about determinants

    This is a proof regarding determinants of elementary matrix and arbitrary square matrix.

  • Continuous, Real Valued, Linearly Dependent Functions and Matrix Determinants

    By our inductive assumption, det_n not= 0, and therefore det( ) not= 0 This completes our full proof. Continuous, Real Valued, Linearly Dependent Functions and Matrix Determinants are investigated.

  • Matrix Proof: Determinants

    12701 Matrix Proof: Determinants Please see the attached file for the full problem description: 1.

  • Matrix Determinants

    Proof: For any nonzero number , we have So the determinant of the matrix is always 0 for any nonzero . A matrix determinant proof is provided. The solution is detailed and well presented.

  • determinants

    441081 proofs about determinants Prove: 1) if A, B are square and AB=I_n, then det B=1/det A 2) if A, B, S are square and B=(S^-1)AS, then det B=det A 3) If A is square and (A^T)A=I_n, then det A= +/- 1 4) if A is n x n and A^T= -A, then det A=

  • Determinant equations

    This is a proof regarding non-colinear points and the equations of a parabola and circle in terms of determinants.

  • Determinant of a matrix

    179013 Determinant of a matrix From Determinants. Please see the attachment. Proof: Suppose is an matrix. Let be the matrix generated by removing the ith row and jth column of .

  • Elementary matrix

    Proof: We consider three types of elementary matrix. We start from the identity matrix . Type 1: is to interchange two rows of . Suppose it interchanges row i and row j, then . Type 2: is to add a multiple of one row to another.

View More Related Solutions