I'm confussed on how to solve this because of the constants a for the given value of s.

Given:

x1 + 0x2 + x3 = a

5x1 + (s-1)x2 + 3x3 = a

sx1 + 0x2 + 4x3 = 1

Find what value of s does the system have on solution?

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- Oct 1st 2012, 07:14 AMnivek0078Find exactly one solution
I'm confussed on how to solve this because of the constants a for the given value of s.

Given:

x1 + 0x2 + x3 = a

5x1 + (s-1)x2 + 3x3 = a

sx1 + 0x2 + 4x3 = 1

Find what value of s does the system have on solution? - Oct 1st 2012, 11:43 AMjohnsomeoneRe: Find exactly one solution
For the general case, a makes no difference:

Have , which is ,

so, when exists, have and it's solved. But exists iff .

Thus, the general condition that will make that system solvable has nothing to do with the B. It's decided by entirely by M, via .

Using cofactors:

.

So when when

Factoring gives , so when .

Thus this is solveable whenever , no matter what a is.

Now, when , it *might* have solutions, but then the value of will decide that.

Check by doing row reduction on:

When you get:

so (used row 1 to clear column 1)

so

so (used row 2 to clear column 3)

Thus and .

The last equation puts a restriction on a: implies implies .

Thus when s = 1, it has a solution, but only if a = 1/7.

The s = 1 and a = 1/7 solution is: .

I'll leave it to you to see what happens when s = 4.