Angličtina pro matematiky II
COURSE MATERIALS WEEK II.
Here is the listening part from week II.
Listening 2
http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/detail/lecture10.htm
Answer the Qs.
1. What are the two important things to do?
2. In what did the lecturer´ s mistake consist?
3. Who reminded him of that mistake?
4. Can the columns be independent? Why yes/no?
5. Which conclusion will this lecture reach?
6. How many subspaces have already been discussed?
Translate:
1) Jednodušší příklad jsem nemohl zvolit.
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2) Měl jsem si toho všimnout dřív.
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3) Takto můžeme shrnout a opravit minulou přednášku.
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4) Nemusela ztrácet čas hledáním vhodné kombinace.
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Transcript - Lecture 10
Listen to the recording again and try to match sentences and gaps.
a) And that makes the columns dependent.
b) So in my innocence, I put in three three eight.
c) I couldn't have taken a simpler example than R^3.
d) I'll have two equal rows and the row space will be only two dimensional.
e) Wait a minute.
f) And why did she say that?
OK, here is lecture ten in linear algebra.
Two important things to do in this lecture.
One is to correct an error from lecture nine.
So the blackboard with that awful error is still with us.
And the second, the big thing to do is to tell you about the four subspaces that come with a matrix.
We've seen two subspaces, the column space and the null space. There's two to go. OK. First of all, and this is a great way to recap and correct the previous lecture -- so you remember I was just doing R^3. 1) ______________________________________
And I wrote down the standard basis.
That's the standard basis. The basis - the obvious basis for the whole three dimensional space.
And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have. It could have linear independence, it could span a space. There's lots of other bases. So I started with these vectors, one one two and two two five, and those were independent. And then I said three three seven wouldn't do, because three three seven is the sum of those. 2) ______________________ I figured probably if three three seven is on the plane, is -- which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane and it's independent and it gives a basis. But after class, to my sorrow, a student tells me, "Wait a minute, that ba- that third vector, three three eight, is not independent." 3) ________ She didn't actually take the time, didn't have to, to find w- w- what combination of this one and this one gives three three eight.
She did something else. In other words, she looked ahead, because she said, 4) _________ if I look at that matrix, it's not invertible. That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows.
I have a square matrix. Its rows are obviously dependent. 5) _____________ So there's my error.
When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows.
And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space. So those are -- the row space is now going to be another one of my fundamental subspaces.The row space of this matrix, or of this one -- well, the row space of this one is OK, but the row space of this one, I'm looking at the rows of the matrix -- oh, anyway,6) _____________________ The rank of the matrix with these columns will only be two. So only two of those columns, columns can be independent too. The rows tell me something about the columns, in other words, something that I should have noticed and I didn't.