# Thread: Linear Algebra help plox?

1. ## Linear Algebra help plox?

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  Reply With Quote

2. ## Re: Linear Algebra help plox?

Gaussian elimination.  Reply With Quote

3. ## Re: Linear Algebra help plox? Originally Posted by He-Mann Gaussian elimination.
can u help ploxx?

Im confused how to get to RRE with t's and numbers, + the rules for one, infinite and no solutions. would be helpful if someone did the question step by step so I understand for subsequent questions.  Reply With Quote

4. ## Re: Linear Algebra help plox?

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.  Reply With Quote

5. ## Re: Linear Algebra help plox? Originally Posted by He-Mann Sorry, I made an error. brb
Ok   Reply With Quote

6. ## Re: Linear Algebra help plox?

Suppose you had a row like this: (0 0 0 | 2317). Would it make sense?  Reply With Quote

7. ## Re: Linear Algebra help plox? Originally Posted by He-Mann 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.
t=4 is that only solution that satisfies a)?

And t not equal to 4 for c)?

what about b)?  Reply With Quote

8. ## Re: Linear Algebra help plox? Originally Posted by He-Mann Suppose you had a row like this: (0 0 0 | 2317). Would it make sense?
Yea I know the no solution part i just was wondering about how to distinguish 1 vs infinite solutions. Something about not having an identity matrix isnt it? then infinite solutions? idk  Reply With Quote

9. ## Re: Linear Algebra help plox? Originally Posted by hayabusaboston Yea I know the no solution part i just was wondering about how to distinguish 1 vs infinite solutions. Something about not having an identity matrix isnt it? then infinite solutions? idk
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).

___

Your solutions are correct for (a) and (c).  Reply With Quote

10. ## Re: Linear Algebra help plox?

It seems that there is no t such that the system yields infinite solutions.  Reply With Quote

#### Thread Information

##### Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•