I have no clue where to go with this matrix:

1 0 k = 1

k 1 0 = 1

0 k 1 = 1

The problem says to find all values of k, if any, for which the system of linear equations has no solution.

x + kz = 1

kx + y = 1

ky + z = 1

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- Feb 5th 2013, 06:46 PMwidenerl194Linear Algebra matrix with variables
I have no clue where to go with this matrix:

1 0 k = 1

k 1 0 = 1

0 k 1 = 1

The problem says to find all values of k, if any, for which the system of linear equations has no solution.

x + kz = 1

kx + y = 1

ky + z = 1 - Feb 5th 2013, 07:41 PMjakncokeRe: Linear Algebra matrix with variables
take the determinant of to get , we want the determinant equal to zero. (Why? Can you anwer this?) so . so the matrix either has zero solutions or infinite solutions. Now how do we know which? Well note that are linearly. independent (the 3rd vector is not independent) so clearly if has a solution at all. which means , but clearly so. for k = -1, no soln. exist.

- Feb 6th 2013, 09:20 AMDevenoRe: Linear Algebra matrix with variables
if k = -1, our system becomes:

x - z = 1 --> x > z.

y - x = 1 --> y > x > z.

z - y = 1 --> z > y > x > z, so z > z, which is impossible.