00:01
The equations given in the problem are minus 2 w plus 2x plus 2y minus 2 z is equal to minus 10.
00:14
Now i'm writing the equations a little bit rearranged as originally given in the question to match the variable serially.
00:24
So we are writing wx y z serially.
00:28
This will help us in forming the matrix.
00:31
So the third equation can be written as 3 w plus x minus y plus 4 z is equal to minus 2.
00:44
Finally, w plus 3x minus 2y plus 2 z is equal to minus x.
00:53
Now these four equations can be written in matrix form and the matrix available will be minus 2, 2, 2, 2 minus 2 minus n, 1, 1, 1, 1, 1, minus 5, 3, 1, minus 1, 4, minus 2, and 1, 3, minus 2, and minus 6.
01:24
And we'll put a dotted line to separate the coefficients and the constant terms of the equation.
01:31
Now our objective will be to transform this matrix into a row echelon matrix.
01:39
So for that we will have to do some row operations.
01:43
The first row operation we will do is we will interchange row 1 with row 2.
01:50
This is done because in row 1 we can see all the terms are 1, especially the first term being 1.
01:58
1 is a factor of all other numbers that must.
02:00
Might be in the first column of all the rows...