Consider the linear system 2x1 + 3x2 - 5x3 - b 7x1 + 2x2 - b2...

  

Transcribed Image Text:

Consider the linear system 2x1 + 3x2 - 5x3 - b 7x1 + 2x2 - b2 -X1 + X2 = b3 +8x3 5x3 - (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 (b1, b2, b3) for which the above system has a solution? (d) If you randomly picked a (b1, b2, b3) in R3, do you expect the above system to have a solution? Consider the linear system 2x1 + 3x2 - 5x3 - b 7x1 + 2x2 - b2 -X1 + X2 = b3 +8x3 5x3 - (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 (b1, b2, b3) for which the above system has a solution? (d) If you randomly picked a (b1, b2, b3) in R3, do you expect the above system to have a solution?

Answer rating: 100% (QA)

a To find the echelon form of the augmented matrix of the system we first write the system in matrix ... View the full answer