Problem 65
Question
What is meant by the order of a matrix? Give an example with your explanation.
Step-by-Step Solution
Verified Answer
The order of a matrix is given by its dimensions, specifically the number of rows followed by the number of columns. For instance, a matrix with three rows and three columns would have an order of \(3 \times 3\).
1Step 1: Definition of Matrix Order
The order of a matrix is a term used to describe the dimensions of a matrix. It is usually expressed by \(m \times n\) where 'm' is the number of rows and 'n' is the number of columns. Thus, the order of a matrix gives us the exact idea of the size of the matrix.
2Step 2: Illustrative Example
For example, consider a matrix \( A = \[ \[ 1, 2, 3 \], \[ 4, 5, 6 \], \[ 7, 8, 9 \] \] \). Here, matrix A has three rows and three columns. Therefore, the order of this matrix is \(3 \times 3\).
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