To solve the repeated addition of vectors step-by-step, let's add each vector component-wise.
Given the vectors:
[tex]\[
\begin{pmatrix}
1 \\
3
\end{pmatrix},
\begin{pmatrix}
1 \\
3
\end{pmatrix},
\begin{pmatrix}
1 \\
3
\end{pmatrix}
\][/tex]
We need to calculate the sum for each component separately:
1. First component (a):
[tex]\[
a = 1 + 1 + 1
\][/tex]
2. Second component (b):
[tex]\[
b = 3 + 3 + 3
\][/tex]
Calculating each:
- For the first component (a):
[tex]\[
1 + 1 + 1 = 3
\][/tex]
- For the second component (b):
[tex]\[
3 + 3 + 3 = 9
\][/tex]
So, the resulting vector from the addition is:
[tex]\[
\begin{pmatrix}
3 \\
9
\end{pmatrix}
\][/tex]
Thus, [tex]\( a = 3 \)[/tex] and [tex]\( b = 9 \)[/tex].
