(1)

The * symbols below represent unknown numbers, and the symbols represent nonzero numbers. The matrix shown represents the augmented matrix for a system of linear equations. Determine if the system is consistent, and if so, determine whether there is a unique solution.

a. (

0

0 0 )

b. (

0 0

0 0 0 )

(2)

[M] In a wind tunnel experiment, the form on a projectile due to air resistance was measured at different velocities:

Velocity (100 ft/sec) 0 2 4 6 8 10

Force (100 lb) 0 2.9 14.8 39.6 74.3 119

Find an interpolating polynomial of the form

() = ₀ + ₁ + ₂² + ₃³ + ₄⁴ + ₅⁵

for these data and estimate the force on the projectile when the projectile is traveling at 750 ft/sec. What happens if you try to use a polynomial of degree less than 5?