Google ad
\[\color {purple} {Example\ 1\ :}\ \color {red}{Find\ the\ determinant\ of}\ A =\begin{bmatrix}
3 & 1 & -1 \\
2 & -1 & 2 \\
2 & 1 & -2 \\
\end{bmatrix}\ \hspace{15cm}\]
\[\color {blue}{Solution:}\ A =\begin{bmatrix}
3 & 1 & -1 \\
2 & -1 & 2 \\
2 & 1 & -2 \\
\end{bmatrix}\ \hspace{15cm}\]
\[\Delta =3\begin{vmatrix}
-1 & 2 \\
1 & -2 \\
\end{vmatrix}\ -\ 1\begin{vmatrix}
2 & 2 \\
2 & -2 \\
\end{vmatrix}\ +\ -1\begin{vmatrix}
2 & -1 \\
2 & 1 \\
\end{vmatrix}\ \hspace{4cm}\]
\[ =3(2\ -\ 2)\ – 1 (-4\ -\ 4) – 1(2\ +\ 2)\
\hspace{10cm}\]
\[ =3(0)\ – 1 (-8) – 1(4)\
\hspace{14cm}\]
\[ =0\ +8 – 4\
\hspace{15cm}\]
\[\Delta =4\
\hspace{16cm}\]
\[\color {purple} {Example\ 2\ :}\ \color {red}{Find\ the\ value\ of\ m\ if}\ \begin{vmatrix}
3 & 4 & -2 \\
-3 & 6 & 2 \\
4 & 1 & m \\
\end{vmatrix}\ =\ 0\ \hspace{15cm}\]
\[\color {blue}{Solution:}\ \begin{vmatrix}
3 & 4 & -2 \\
-3 & 6 & 2 \\
4 & 1 & m \\
\end{vmatrix}\ =\ 0\ \hspace{15cm}\]
\[3\begin{vmatrix}
6 & 2 \\
1 & m \\
\end{vmatrix}\ -\ 4\begin{vmatrix}
-3 & 2 \\
4 & m \\
\end{vmatrix}\ -2\begin{vmatrix}
-3 & 6 \\
4 & 1 \\
\end{vmatrix}\ =\ 0\ \hspace{4cm}\]
\[ 18m\ -\ 6\ +\ 12m\ +\ 32\ – 2(-27)\ =\ 0\
\hspace{14cm}\]
\[3(6m\ -\ 2)\ -\ 4 (-3m\ -\ 8)\ -\ 2(-3\ -\ 24)\ =\ 0\
\hspace{10cm}\]
\[ 30m\ +\ 26\ +\ 54\ =\ 0\
\hspace{14cm}\]
\[ 30m\ =\ -\ 80\
\hspace{14cm}\]
\[ \boxed{m\ =\ \frac{-8}{3}}\
\hspace{14cm}\]
Google ad
Google ad
Google ad
Google ad