Activity 1
- Solve the following matrix-vector product equation:
$$
\begin{bmatrix}
3 & -1 & 4\\
6 & -4 & 12\\
-1.5 & -5.5 & 12
\end{bmatrix}
\cdot
\boldsymbol{x}
=
\begin{bmatrix}
2\\
-1\\
5
\end{bmatrix}
$$
-
Find $x_1$, $x_2$, $x_3$ such that
$$
x_1 \cdot
\begin{bmatrix}
1\\
-4\\
2
\end{bmatrix}
+
x_2 \cdot
\begin{bmatrix}
-5\\
22\\
-14
\end{bmatrix}
+
x_3 \cdot
\begin{bmatrix}
3\\
-17\\
19
\end{bmatrix}
=
\begin{bmatrix}
1\\
1\\
1
\end{bmatrix}
$$
-
Find all solutions to the following linear system of equations:
$$
\begin{array}{rcrcrcc}
x_1 & - & 3 x_2 & + & 2 x_3 & = & 3\\
-4 x_1 & + & 16 x_2 & - & 11 x_3 & = & 2\\
2 x_1 & - & 14 x_2 & + & 10 x_3 & = & 3
\end{array}
$$