Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.) S = {(3, 2), (−1, 1), (4, 0)}

The solution is explained below

Explanation

What you want to do here is use Gauss-Jordan elimination to find the reduced row echelon form. Then you'll see that there is at least one column without a leading 1. Then your first column represents a₁, your second a₂, and 3rd is a₃. Whichever column(s) doesn't have a leading 1, you can set that variable equation to an arbitrary value.

Then solve for a₁ and a₂ in terms of t. For the matrix, you'd have a₁=0−3t=−3t, a₂=0−t=−t and a₃=t. Whatever you get at this point will be the general solution.

no sign of dia of fuel cell

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft