Certainly! Let's solve the problem step by step.
1. Understand the problem: We are asked to multiply a binomial vector by a scalar and represent it as a column vector. The binomial vector in this case is [tex]\(\binom{2}{5}\)[/tex], and the scalar is [tex]\(3\)[/tex].
2. Identify the elements: The binomial vector has two elements: [tex]\(2\)[/tex] and [tex]\(5\)[/tex], and the scalar given is [tex]\(3\)[/tex].
3. Multiply the scalar with each element:
- Multiply the scalar [tex]\(3\)[/tex] with the first element of the binomial vector:
[tex]\[
3 \times 2 = 6
\][/tex]
- Multiply the scalar [tex]\(3\)[/tex] with the second element of the binomial vector:
[tex]\[
3 \times 5 = 15
\][/tex]
4. Formulate the column vector: To write this as a column vector, we place each of the resulting numbers in a vertical arrangement:
[tex]\[
\begin{pmatrix}
6 \\
15
\end{pmatrix}
\][/tex]
So, the scalar [tex]\(3\)[/tex] multiplied by the binomial vector [tex]\(\binom{2}{5}\)[/tex] written as a column vector is:
[tex]\[
\begin{pmatrix}
6 \\
15
\end{pmatrix}
\][/tex]
