00:01
In this question, we are asked to solve the given systems of equations and classify them as consistent, inconsistent, dependent and independent.
00:10
In the first case, the first line of the matrix corresponds to the equation x1 equals 6.
00:18
The second line corresponds to x2 equals to negative 3.
00:22
The third line corresponds to x4 equals 5.
00:26
And the last line corresponds to 0 equals 0.
00:29
Note that there is no x3 in this equation, and that means that x3 is a free variable, meaning x3 can be any number.
00:41
We can write that solution in vector form as x equals to the constant vector 6 -negative 3, 0, 5, that's the constant vector, plus the vector containing the free variable.
01:07
That's going to be 0 -0 -1 -0 multiplied by x3.
01:16
So this is a solution of the given system of equations.
01:20
And since it has a solution, we conclude that it's consistent.
01:28
And since there is a free variable, the equation is dependent.
01:39
So this is a solution, and yeah, this is a classification.
01:47
Alright, let's move on to the next one.
01:51
In the second case, the first equation corresponds to x1 equals 2...