Prove or Disprove: Let A ∈ Mn×n(R) be a matrix such that A^n = 0 for some n ∈ Naturals. Then could λ = 2 be an eigenvalue of A?

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

The quadratic function h(t) = -16.1t^2 + 150 models a balls height, in feet, over time, in seconds, after its dropped from a 15 story building. from what height in feet was the ball dropped?

Afruit stand has to decide what to charge for their produce. they need $10 for 4 apples and 4 oranges. they also need $15 for 6 apples and 6 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange?