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Q: When adding or subtracting matrices do the dimensions of the sum or differences always match the original matrices?

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a

The same as the original vector. The scalar will change the numbers, but not the dimensions.

It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b

There are no differences

adding the additive identity matrix does not change the original matrix

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no there are multiply differences

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it means multiplying the original number by two and then subtracting two, like if your original number was 10, 10 times two equals 20 minus 4 equals 16.

These are called the second differences. If they are all the same (non-zero) then the original sequence is a quadratic.

In the marine industry, when something is re-cladded, it is a metal that has been built up to original dimensions. For example, a tail shaft is eroded. To effect a repair, the shaft is machined down past the erosion and pitting. Then the shaft is built up again using submerged arc welding to original dimensions where it would be machined to the final dimensions. We would say then the the shaft had been re-cladded.

Presumably, both the original matrices and the result matrix would be stored in 2-dimensional arrays; to do the actual addition, write two "for" loops, one for each row, and one for each column. Inside the inner "for" loop, just add the corresponding elements and place the result in the result matrix.

A replacement part should be of the same dimensions.

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There are no differences. The Catholic Church is the original Christian Church and is the only Church which still holds to all the Christian truths as handed down by the Apostles.

the dimensions of the cylinder would be 2 times greater. We just had a test on this stuff and this was one of the questions.

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