I'm getting 4^4 but my book says 3*(4^4) .
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The book is counting 2*2, 1*4 and 4*1 matrices.
Personally I think they're being a bit too sneaky. The section is presumably probability, so why are they asking you to remember the different types of matrices.
Personally I think they're being a bit too sneaky. The section is presumably probability, so why are they asking you to remember the different types of matrices.
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If a matrix has 4 symbols and you form one matrix at a time and you can reuse symbols, I believe that it is 4^4.
Basically, the question is, "how many base 4 numbers can you represent in 4 base 4 digits?" If you think about the same problem in base 10, 10 digits, 10 symbols with reuse (essentially, counting) then the answer is obviously 10^4. So this same problem in base 4 is 4^4.
The only possibility for 3*4^4 is if they show that there are three of these matrices at the same time.
OK, I read Paula's answer and she is technically right, there are three shapes of matrices you can form with four elements that are not sparse, 1x4, 2x2 and 4x1 so that is why it is 3*4^4. I also agree that it is odd that they would not mention that in a probability section.
Basically, the question is, "how many base 4 numbers can you represent in 4 base 4 digits?" If you think about the same problem in base 10, 10 digits, 10 symbols with reuse (essentially, counting) then the answer is obviously 10^4. So this same problem in base 4 is 4^4.
The only possibility for 3*4^4 is if they show that there are three of these matrices at the same time.
OK, I read Paula's answer and she is technically right, there are three shapes of matrices you can form with four elements that are not sparse, 1x4, 2x2 and 4x1 so that is why it is 3*4^4. I also agree that it is odd that they would not mention that in a probability section.