The number of all possible matrices of order 3×2 with each entry 1 or 2 is :
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Step-by-Step Solution
Step 1: Understand Matrix Order and Entries
A matrix of order 3×2 has 3 rows and 2 columns. This means there are a total of 3×2=6 positions or entries in the matrix.
Step 2: Determine Choices for Each Entry
Each entry in the matrix can be either 1 or 2. So, for each of the 6 positions, there are 2 possible choices.
Step 3: Calculate Total Number of Matrices
Since each of the 6 entries can be chosen independently from 2 options, the total number of possible matrices is found by raising the number of choices per entry to the power of the total number of entries.
Step 4: Compute the Result
Calculating 26 gives us 64. Therefore, there are 64 possible matrices of order 3×2 where each entry is either 1 or 2.