00:01
Okay, here are my three plane equations.
00:04
What i've done with the second two is simply taken this number from the left -hand side to the right -hand side, and likewise here.
00:12
It was plus 10 in the question, make it minus 10 on the right -hand side.
00:18
So get the x, y, z terms alone on the left, makes life easier.
00:22
Now, i can write this in matrix form, which is going to be 1, 2, negative 1, 1k minus 3, 2, 1, 1.
00:36
These here are the coefficients of x, y, and z, like 1 here, 2, negative 1, and so on, times x, y, z equals 0 minus 11 minus 10.
00:56
Now, this matrix equation will always have a solution as long as this has an inverse.
01:04
Now, for an inverse, what you can't have is a zero determinant.
01:13
So we need the determinant of that matrix, 1, 2, negative 1, 1k minus 3, 2, 1, 1.
01:24
That just cannot be zero.
01:27
If it's zero, we get no single solution.
01:30
We get either no solution at all or infinite solutions.
01:36
So this then i can work out.
01:40
What i do, it'll be 1 times k plus 3.
01:45
What i'm doing here is i'm removing this line, that row, that column, and it's 1 times this determinant, which is k times 1 minus 1 times minus 3.
01:59
Now, that you should know already.
02:03
Then we have minus 2...
