Gaussian elimination.
I just registered for a maths diploma and they accepted me only now after two full weeks so im trying to catch up on content
How u do dis?
2. Determine the values (if any) of t in R for which the following linear system has:
(a) no solutions,
(b) infinitely many solutions,
(c) a unique solution.
In the case (b) of infinitely many solutions, find all solutions.
tx-5y+3z=-8t
-tx+8y+3tz=11t
-x+2y+3z=1
Gaussian elimination.
Do row operations as usual, group up the rows containing t to make it easier to analyse.:
There's probably a faster sequence of row operations to reach RREF, but that's one way.
Start with (a), what values of t produces a contradiction? That's when you cannot solve the system.
Last edited by He-Mann; 6 Aug 2017 at 3:26 PM.
Suppose you had a row like this: (0 0 0 | 2317). Would it make sense?
If you want to get infinite solutions, then you need to prevent at least one row from giving any information. Intuition: for RREF, each row should give information about one of x, y, or z. But when you stop one row from finding either x, y, or z, then you won't be able to solve other rows. e.g., solving for y and z in y+z = 2 when you don't have any information on y or z. Thus, you get infinite solutions for y and z.
i.e., produce a zero row (0 0 0 | 0).
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Your solutions are correct for (a) and (c).
Last edited by He-Mann; 6 Aug 2017 at 4:20 PM.
It seems that there is no t such that the system yields infinite solutions.
Last edited by He-Mann; 6 Aug 2017 at 4:16 PM.
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