Suppose t : r r3 is an onto linear transformation. list all of the possible echelon forms of the standard matrix for t. use the notation of problem three above. 5. if a linear transformation t: ra+ rb is one-to-one, what must be true about a and b? i. e. can you give a relation between a and b? explain the reason for your answer using complete sentences. ro is onto, what must be true about a and b? ie. can you give a relation 6. if a linear transformation t: ra between a and b? explain the reason for your answer using complete sentences.

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3