Order of First Row and Second Column of a Matrix
Question:
Let \( A \) be a matrix of order \( 3 \times 4 \). If \( R_1 \) denotes the first row and \( C_2 \) denotes the second column, find their orders.
Concept Used
The order of a matrix is given by number of rows × number of columns. :contentReference[oaicite:0]{index=0}
– A row matrix has order \( 1 \times n \) – A column matrix has order \( n \times 1 \) :contentReference[oaicite:1]{index=1}
Step 1: Given Matrix
\[ A \text{ is of order } 3 \times 4 \]
This means:
- 3 rows
- 4 columns
Step 2: Order of First Row \( R_1 \)
The first row contains all columns → total 4 elements.
So, \( R_1 \) is a row matrix:
\[ R_1 = 1 \times 4 \]
Step 3: Order of Second Column \( C_2 \)
The second column contains all rows → total 3 elements.
So, \( C_2 \) is a column matrix:
\[ C_2 = 3 \times 1 \]
Final Answer
Order of \( R_1 = 1 \times 4 \)
Order of \( C_2 = 3 \times 1 \)