Consider the linear system 211 + 3x2 - 5.23 = b 7.01 + 2.02 + 813 = b2 -x1 + 12 - 5.23 = b3

(a) find the echelon form of the augmented matrix of the above system.

(b) find the conditions on b1,b2, b3 for which this system has a solution.

(c) do you see the shape of the points (61, 62, 63) for which the above system has a solution?

(d) if you randomly picked a (61, 62, 63) in r3, do you expect the above system to have a solution?

The answers are shown in the step by step explanation that is attached

Step-by-step explanation:

The step by step calculation is as shown in the attachment below

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: