(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given

[tex]A[/tex] = [tex]\left( \begin{array}{cc}

2 & 1 \\

6 & 4 \end{array} \right)[/tex]

a) Express A as a product of elementary matrices.

b) Express the inverse of A as a product of elementary matrices.

2. Relevant equations

3. The attempt at a solution

Using the following EROs

Row2 --> Row2 - 3 * Row1

[tex]E_{1}[/tex] = [tex]\left( \begin{array}{cc}

1 & 0 \\

-3 & 1 \end{array} \right)[/tex]

Row1 --> 1/2 * Row1

[tex]E_{2}[/tex] = [tex]\left( \begin{array}{cc}

1/2 & 0 \\

0 & 1 \end{array} \right)[/tex]

Row1 --> Row1 - 1/2 * Row2

[tex]E_{3}[/tex] = [tex]\left( \begin{array}{cc}

1 & 0 \\

-2 & 1 \end{array} \right)[/tex]

Multiplying all the Elementary matrices together, I got the Product

[tex]P[/tex] = [tex]\left( \begin{array}{cc}

2 & -1/2 \\

-3 & 1 \end{array} \right)[/tex]

Which is A^{-1}.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Given a Matrix A, find a Product of Elementary Matrices that equals A

**Physics Forums | Science Articles, Homework Help, Discussion**