Adding and subtracting matrices
1 answer:
We can only sum matrices with equal order, so we can't sum matrices A and B in the first exercise.
As for the second exercise, we have:
- False
- True
- True
- True
- True
- False
All of these answers depend on the fact that the sum/difference of two matrices is simply the sum/difference of the correspondent elements. So, if the element in the i-th row and the j-th column of A is and the element in the i-th row and the j-th column of B is
, we have
So, the sum between matrices inherits the properties of the sum between numbers: the order matters when you subtract (which is why a and f are false), the sum is commutative (which is why b, c, d are true) and associative (which is why e is true).
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each have two twos. both have one 5, so we know our answer will look something like
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one has one 3 and one has two, so we need two threes. now our equation is
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how many sevens does 60 have? 0, and 630 has 1, so we know we need one 7. our answer becomes
to find the least common multiple, you need to first figure out what the prime factors have in common.
each have two twos. both have one 5, so we know our answer will look something like
now to figure out the other stuff... we have to represent the greatest amount of everything that is left, and we have 3s and 7s left over, so we need to figure out how many of each we need.
one has one 3 and one has two, so we need two threes. now our equation is
what's the only number we have to deal with? 7...
how many sevens does 60 have? 0, and 630 has 1, so we know we need one 7. our answer becomes