Column Matrix & Scalar Multiplication
Question:
In a city, there are 30 colleges. Each college has:
In a city, there are 30 colleges. Each college has:
- 15 peons
- 6 clerks
- 1 typist
- 1 section officer
Solution:
Step 1: Column Matrix Representation
\[ A = \begin{bmatrix} 15 \\ 6 \\ 1 \\ 1 \end{bmatrix} \]Step 2: Multiply by number of colleges (30)
\[ 30A = 30 \begin{bmatrix} 15 \\ 6 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 450 \\ 180 \\ 30 \\ 30 \end{bmatrix} \]Interpretation:
- Peons = 450
- Clerks = 180
- Typists = 30
- Section Officers = 30
Final Answer:
\[ \boxed{ \begin{bmatrix} 450 \\ 180 \\ 30 \\ 30 \end{bmatrix} } \]