Examples of using Augmented matrix in English and their translations into Polish
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I will create an augmented matrix.
So the augmented matrix would look like that.
So let me rewrite my augmented matrix.
So what's the augmented matrix for this system of equations?
Now we can just solve this with an augmented matrix.
So let's construct the augmented matrix for this system of equations.
And we just got this from our technique of creating an augmented matrix whatnot.
Let me rewrite my augmented matrix in the new form that I have.
And the way you would solve it-- and we have done this many times, this was many videos ago-- you would make an augmented matrix with this.
First I would make an augmented matrix of it.
If we call this augmented matrix, matrix A, then I want to get it into the reduced row echelon form of matrix A.
So what you want to do is, eventually,get your augmented matrix to look like this.
We can set up an augmented matrix that looks like this, where you put A on this side, and then you put the vector b on the right-hand side.
And we do our reduced row echelon form with this augmented matrix, and A goes to its reduced row echelon form.
But what I'm doing from all of these steps,I'm essentially multiplying both sides of this augmented matrix, you could call it, by a inverse.
Now, I want to get this augmented matrix into reduced row echelon form.
Anytime you just want to solve the equation Ax is equal to b-- and remember, we want to make sure that this can be true for any b we chose-- what we could do is we just set up this augmented matrix like this, and we perform a bunch of row operations until we get A, we get this matrix A to reduced row echelon form.
So let's go back from the augmented matrix world and kind of put back our variables there.
What I'm going to do is I'm going to solve it using an augmented matrix, and I'm going to put it in reduced row echelon form.
Hopefully this at least gives you a decent understanding of what an augmented matrix is, what reduced row echelon form is, and what are the valid operations I can perform on a matrix without messing up the system.
And so when you when you go back to your-- I guess when you go out of the augmented matrix world and rewrite it as a system, and you solve for it, and we did this in the last video-- you will get your solution set.
We're performing on the entire row of these augmented matrices.
We have both of these augmented matrices in reduced row echelon form.
And like the first video, where I talked about reduced row echelon form, andsolving systems of linear equations using augmented matrices, at least my gut feeling says.