Question

**please choose your favorite, unique 3x3 Matrix
A** containing no more than two 0 entries and having a
**nonzero** determinant. I suggest choosing a matrix
with integer elements (e.g. not fractions or irrational numbers)
for computational reasons.

- What is your matrix A? What is det (A)?
- What is A
^{T}? What is det (A^{T})? - Calculate A A
^{T}. Show that A A^{T}is symmetrical. - Calculate A
^{T}A - Calculate the determinant of (A A
^{T}) and the determinant of (A^{T}A). Should the determinants be equal? Why or why not? - Find the inverse of A using the method: [A | I ] → [ I |
A
^{-1}]. Set up and then use a calculator (recommended). Express the elements of A^{-1}as fractions if they are not already integers. (Use*Math -> Frac*if needed.) - Begin the LU factorization of A by determining a first
elementary matrix E1 and its inverse E1
^{-1}. Identify the**associated row operation**. (That is all. You do**not**need to complete the LU factorization for the exam.)

Answer #1

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