00:01
For our next problem, we want to show that the matrix a, which is this very big matrix, we have entries 0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -g, and 0 -0 -0 -0 -0 -0 -0 -0 -g, and 0 -0 -0 -h0 -0 -0 -0 -0 -0 -0 -0 -g, and 0 -0 -0 -h0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -h -0 - is not invertible.
00:40
And so recall so far we know a matrix x is invertible if we can write down x inverse such that x x inverse equals x inverse x equals the identity.
01:02
The reduced row echelon form of x is the identity or x times some vector y equals the zero vector only has solution y equals zero with the zero vector.
01:28
And so it turns out that this reduced row echelon form is probably the fastest way to show that an arbitrary matrix is not invertible.
01:40
So if the reduced row echelon form has any row of zeros, it's not invertible.
01:55
And looking at a, there are a couple of row operations to show that you do indeed get a row of zero.
02:05
So first of all, we want to examine this row a and this row h.
02:13
And if a equals zero or h equals zero, we're done...