Assuming the standard definitions of addition and scalar multiplication, decide whether or not the following sets are vector spa
ces.Justify your answers by verifying that all properties of a vector space are satisfied or that at least one of the properties fails to hold.(a) The setVof all3×3lower triangular matrices (all entries above the main diagonal are zero).(b) The setVof all2×2matrices whose determinants are 0.
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Answer:
There are 650 cannonballs
Step-by-step explanation:
If you look closely in the picture, you can see that:
- 1st row has 1 ball
- 2nd row has 4 balls
- 3rd row has 9 balls
- 4th row has 16 balls
etc. etc.
We can see that the number of balls is the square of the row number. There are a total of 12 rows. So, rest of the rows has:
- 5th row has 25 balls
- 6th row has 36 balls
- 7th row has 49 balls
- 8th row has 64 balls
- 9th row has 81 balls
- 10th row has 100 balls
- 11th row has 121 balls
- 12th row has 144 balls
If we add up all those, we get total number of balls:
There are 650 cannonballs