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Fix Question 4

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Ceda EI 2020-05-13 12:09:12 +05:30
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maths/assignment-matrices/assign2.tex
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@ -197,31 +197,31 @@ Reduce the matrix \(A =
To convert it into Echelon form, we apply the following transformations.
\begin{align*}
R_1 &\to R_1 + R_2 + R_3 \\
R_2 &\to R_2 - R_3 \\
C_2 &\to C_2 + C_4 \\
C_4 &\to C_4 + C_3 \\
C_4 &\to C_4 - 2 C_1 \\
C_3 &\to C_3 - C_2 \\
C_2 &\to C_2 - C_1 \\
R_2 &\to \frac{R_2}{2} \\
R_1 &\to R_1 + R_2 \\
R_1 &\leftrightharpoons R_4 \\
C_4 &\leftrightharpoons C_1 \\
R_4 &\to R_4 - R_2
R_2 &\to R_2 - R_3 \\
R_2 &\to \frac{R_2}{2} \\
R_3 &\to R_3 + R_4 \\
R_2 &\to R_2 - R_1 \\
R_3 &\to R_3 - R_1 \\
R_3 &\leftrightharpoons R_4 \\
R_2 &\leftrightharpoons R_3 \\
R_1 &\leftrightharpoons R_2 \\
R_1 &\to -R_1
\end{align*}
We get
\[
\begin{bmatrix}
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
1 & -1 & 0 & 2 \\
0 & 1 & 1 & -1 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix}
\]
\[
rank = 3
rank = 2
\]
\section*{Question 5}