1)There are 4 switches numbered 1 through 4. Is it possible to set the switches such that:

i) Switch 3 is off.

ii) An odd number of switches 1, 2 and 3 are OFF.

iii) An odd number of switches 2, 3 and 4 are ON.

iv) An even number of switches 1 and 3 are ON.

Switch 1: ?

Switch 2: ?

Switch 3: ?

Switch 4:?

2)Find a non-trivial solution to the following homogeneous system of equations:

(4+i)x −1y = 0

(−18+4i)x +(4−2i)y = 0

3)A student finds $1.05 in dimes, nickels

and pennies. If there are 17 coins in all, how many coins of each

type can he have?

This is what i got..

0.10 x + 0.05 y + 0.01 z = 1.05

x + y + z = 17 ,

The first question, I have no idea how to do it....

For second, I tired to use matrix, but the answer doesn't make sense to me. the answer have to be in a+bi form...

The third , I don't know what to do next, because there is infinite solution... but how can I find all the solution?

Please help me...

ty!