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oleifere45

oleifere45

Answered question

2022-06-16

| 1 2 5 4 5 8 3 3 3 | | x 1 x 2 x 3 | = | b 1 b 2 b 3 |
I need to determine the values of the b constants that would guarantee that the linear system is consistent. I tried to find the inverse of the matrix on the left hand side so that I could try and solve for the x variables and see if there are any values of b that would cause the system to be inconsistent but the matrix is singular. I then went on to put the matrix in reduced row echelon form.
| 1 0 3 0 1 4 0 0 0 |
From this I was able to derive the equations: x 1 3 x 3 = b 1 , x 2 4 x 3 = b 2 , and 0 = b 3 . I know that the answer is b 1 = b 2 + b 3 , but I don't know how to get that with the given information.

Answer & Explanation

Schetterai

Schetterai

Beginner2022-06-17Added 25 answers

When you do Gaussian elimination to reduce the matrix to its row echelon form, you should include the vector b in it. So the same operations will be done on b.

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