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s3w6 FC Matrix inverses and determinents

Last updated 5 months ago

11 questions

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Question 1

1.

We should have done matrices last year. Lets see what we remember. What are the dimensions of this matrix?

[4 x 3]

[3 x 4]

12

Question 2

2.

What is the address of the -circled 2 ?

Question 3

3.

add these two matrices, you can try sketching, but i would use text or math and just move stuff around.

Question 4

4.

Perform the following matrix operation:

Question 5

5.

This is a video on the procedure for finding the determinant of a matrix. It is a pretty simple formula, but if you want a step through, this will help. do you have any questions?

Question 6

6.

The identity property of multiplication is that
And while
is true, it isn't useful. There is an identity property of multiplication of matrices. and this is
in this case I is the

identity matrix - a square matrix of all ones

identity matrix - a matrix of any size of all ones

Identity matrix - a square matrix of mostly 0s, with a diagonal of ones from top left to bottom right

Identity matrix - a square matrix of all 0 with a diagonal of ones from top right to bottom left

Question 7

7.

There is no matrix division, so you cannot say

But what you can say is that

is the inverse of A. To find how to find in the inverse you can watch this video.

Question 8

8.

ok, you will have noticed that this is a pretty light week. That is because the only videos I could find about determinants and matrices were fairly straight-forward "here's how ya do this" type videos, with pretty much no conceptual backing. I did find some EXCELLENT conceptually backing videos, but they are... dense. So, I have tried to make the aleks homework very very simple and short. These videos don't explain how to do the math at all, they are more about trying to visualize what matrices are trying to accomplish. My hope with these is that you have a better understanding of what is happening graphically with matrices. And, if nothing else, these videos are really pretty. Here is the first one, it is hopefully mostly review: respond with any questions you might have.
Also: don't watch all these at once, spread them out a bit. as I said, they are kinda dense.

Question 9

9.

Here is the second, it may help to think of span like the range of a function, except the function has sliders for all its constants. thoughts and questions?

Question 10

10.

I think this will be the hardest one. maybe. Do what you can. I mentioned in class that a vector was a sort of subspecies of matrix. a one column, or one row matrix. This is a very visual way of getting us to the "exactly what is it we are doing here" when working with matrices, and it will give you a way of thinking of matrices as sets of vectors working together for a purpose.

Question 11

11.

Ok, last one. This one is hopefully going to give you a better foundation for what it means to take the dot product of matrices. One of the ways you know the dot product isn't really multiplication is because there is no division. It is not simply scaling the vector. So what is it?