A homogeneous solution.

A times our any solution minus A times our particular solution.

Now, if we just add our particular solution to both sides of this, we get that any solution remember, we assume that x is any solution to this that any solution is equal to our homogeneous solution, is equal to a homogeneous solution, plus a particular solution or plus our particular solution.

Which statement about Stan's solution is true?

So A times this guy right here, times some particular solution, plus some homogeneous solution is going to be equal to A times the particular solution, plus A times some member of my null space.

let me write it in blue any solution takes the form if there is a solution.

They don't have another thing they can do.

That would be the solution, the vector solution to this equation.

Now, we just said that any solution to an inhomogeneous

So what I implied in the last video, and I didn't show it to you rigorously, is that any solution to the inhomogeneous system let me write it this way, any solution and do it in white that's not white any solution to the inhomogeneous system Ax is equal to b, this is a claim I made, will take the form some particular solution that was this right here, maybe I should do it in green this is this right here When you do the reduced row echelon form, it becomes that b prime vector.

So does any solution x, to Ax equal to b, take the form x is equal to some particular solution, plus a member of our null space, or plus a homogeneous solution.

And once you know this you are ready to tackle any type of multiplication problem.

let's say that x is any solution to Ax is equal to b.

That this is a solution to our inhomogeneous equation, and that any solution to our inhomogeneous equation takes this form right here.

But if there is a solution, any solution is going to take the form x particular plus a member of your null space.

So it is on the line it is a solution. x 3, y 4 is a solution to this equation.

Any solution if they exist, if there are no solutions, that's fine.

I have a solution that requires neither machine, nor wood, nor cooking gas.

So this would imply that this equation we're trying to set up, Ax is equal to b1, has no solution.

But the way we solve them is with humility to abandon the God complex and to actually use a problem solving technique that works.

It says, which statement best explains why there's no real solution to the quadratic equation?

Now the next question is, does every solution to the inhomogeneous system, or does any solution to the inhomogeneous system, take this form?

And of course, any particular solution to this when you multiply it by A is also going to be equal to b.

He made me feel we were both smart, and the two of us could solve any problem whatever.

But the way we solve them is with humility to abandon the God complex and to actually use a problem solving technique that works.

Or another way to think about it is, x, the vector x minus our particular solution is a solution to A times x is equal to 0.

Now you show me a successful complex system, and I will show you a system that has evolved through trial and error.

Anyway, I hope you can do the module now and maybe I'll add a few more presentations because this isn't the easiest module.

So you can say that x minus so our any solution x minus the particular solution of x is a member of our null space.

You go to any factory, any power plant, any chemical plant, any food processing plant, you look around everything is being run by computers.

And if you have problems with this, you might just want to try just the slope of the line problems or the y intercept problems separately.

So, since its a member of our null space, we can say that it is equal to so our any solution minus our particular solution is equal to some member of our null space.

Well we know that the only solution to this is that they all equal 0 because anything that's a solution to this is a solution to this.

Of course, implementing such a solution will not be easy not least because of sharp divisions among relevant external powers. Like Russia, Iran which will be crucial to the success of any solution backs the regime.

Name anyone, name, please, any suit.

Bread? What bread? Sound?

It's equal to 10 squared, which is equal to 100.

So in order for our transformation to be one to one, that means if you pick any b here, there has to be, at most, one solution to Ax is equal to b.

So it's going to be 7 times 10, so 70, plus 7 times 10 plus 5 times 12, plus 60.

I could label frankly any, any number right over here

Which is 4, minus the second x, which is that 1.

What?

Yeah..

Y yes ?

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