Solve the problem. Question 6 options: Equation is consistent for all b 1 , b 2

Question

Solve the problem.

Question 6 options:

Equation is consistent for all b1, b2, b3 satisfying -3b1 + b3 = 0.

Equation is consistent for all b1, b2, b3 satisfying 2b1 + b2 = 0.

Equation is consistent for all possible b1, b2, b3.

Equation is consistent for all b1, b2, b3 satisfying 7b1 + 5b2 + b3 = 0.

please show your work when you answer the question

Equation is consistent for all b1, b2, b3 satisfying -3b1 + b3 = 0.

Equation is consistent for all b1, b2, b3 satisfying 2b1 + b2 = 0.

Equation is consistent for all possible b1, b2, b3.

Equation is consistent for all b1, b2, b3 satisfying 7b1 + 5b2 + b3 = 0.

please show your work when you answer the question

1-32 -25-1 3-4-6 2-1-6 123

Explanation / Answer

The augmented matrix of the system is B =

1

-3

2

b1

-2

5

-1

b2

3

-4

-6

b3

We will reduce B to its RREF as under:

1.Add 2 times the 1st row to the 2nd row; 2.Add -3 times the 1st row to the 3rd row

3.Multiply the 2nd row by -1; 4.Add -5 times the 2nd row to the 3rd row

5.Multiply the 3rd row by 1/3; 6.Add 3 times the 3rd row to the 2nd row

7.Add -2 times the 3rd row to the 1st row; 8.Add 3 times the 2nd row to the 1st row

Then the RREF of B is

1

0

0

1/3(34b1+26b2+7b3)

0

1

0

5b1+4b2+b3

0

0

1

1/3(7b1+5b2+b3)

Apparently, the equation Ax = b is consistent for all possible b1,b2,b3. If x = (x,y,z)T, the solution is x = 1/3(34b1+26b2+7b3), y = 5b1+4b2+b3 and z= 1/3(7b1+5b2+b3).

1

-3

2

b1

-2

5

-1

b2

3

-4

-6

b3

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