one way to do this is to turn them into a system of equations.
you want t=xu+yv+zw, with x, y, and z as your unknowns.
take 6=4x+5y+z
-13=-x+3y-z
14=2x +2z
the x components go with the u values, the y components go with the v values, and the z components go with the w values
now, solve this system of equations and plug it back into the equation t=xu+yv+zw to show it as a LC. hope this is helpful.
for the 2nd question, do you know about free variables versus fixed variables? if there are any free variables after row reducing the sets, meaning more than one nonzero number in a column, then it is linearly dependent. to get a linearly independent answer, you want 1's on the main diagonal and 0's everywhere else.