TERRI F.

asked • 04/23/17

How do I work this?

Find the values of a and b such that the following system has solution (1, −2, 3).
[1     a     b     1]
[2b  2a   5     13]
[2a  7     3b   −8]

Mark M.

I suspect, could be wrong, that the order should be "a," "b," then constant. 
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04/23/17

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Mark S. answered • 04/23/17

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Hint: Given the solution and the first row of the matrix...you should be able to determine an easy relationship between "a" and "b" and then substitute accordingly!
 
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Mark M.

Taking your hint
1 + a + b = 1
a + b = 0
b = -a
Then
2b + 2a + 5 = 13
-2a + 2a + 5 = 13
0 + 5 = 13
Ooops.
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04/23/17

Mark S.

You are mistaken.
Your conclusion that b=-a is not the correct conclusion from my hint.
 
The problem is correct as stated. I don't like to give solutions, so here is another hint:
It is not 1 + a + b = 1 as you wrote...you forgot the variables that the matrix drops
 
Try x + ay + bz = 1 instead (and the information from the solution matrix) and then you will see the correct relationship between a and b is ay = bz !
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04/23/17

Mark S.

typo.... ay=-bz
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04/23/17

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