v. This theorem provides a new method for finding inverses when they exist: substitute the matrix into the characteristic polynomial to get the equation guaranteed by your theorem, then solve for A-1 (potentially using factor- ing.) Demonstrate this technique by performing it on both nontrivial 2 x 2 and 3 x 3 matrices of your choice and comparing your inverses with those you determine by another method (such as just checking with Sage).

Q: Use Gauss-Jordan method to calculate the inverse of A A-l = |1 0 -1 A =| 0 1 1 1 1 1

A: By Gauss Jordan Elimination method the inverse of matrix is given as follows :

Q: Q4: Using Cayley - Hamilton theorem to find the inverse of the matrix A, where 1 1 2 A = 3 1 1 2 3 1

A:

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: Verify by direct multiplication that the given matrices are inverses of one another. 4 -7 4 2 7 -1

A: GIVEN : A = 1427            A-1 = -7   42-1

Q: Please answer this linear algebra question and show all steps.

A: The final answer given below:Explanation:

Q: Find the characteristic equations of the following matrices: 401] -210 -201

A:

Q: (i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices,…

A:

Q: Let A be an (m n) matrix then nullity(A) + rank(A) = = m. False O True

A: The objective is to find true or false of the above statements.

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p2(x) as…

A: The given polynomial is p(x)=x2-9 and p1(x)=x+3 ,p2(x)=x-3 We have to prove that p(A)=p1(A)p2(A)