There are ten kids in a class. When any two meet, they shake their hands. Before the class starts, how many handshakes are there?

45

Step-by-step explanation:

Ok, Kid 1 can meet other 9 kids, so we have 9 handshaks.

Kid 2 can also meet other 9 kids, but he already meet kid 1, so we are not counting that handshake, this means that now we have 8 handshakes.

Kid 3 can also meet 9 kids, but we already counted the handshake with kid 1 and kid 2, so here we have other 7 andshakes.

And so on, so we have a total of:

9 + 8 + 7 + 6 + 5 + 4 +3 + 2 + 1 = 45 handshakes in total.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,