- #1
WTFsandwich
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Homework Statement
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.
Homework Equations
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.
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