# Linear algebra again.

1. Feb 9, 2008

### frasifrasi

Ok, so I grasped how to some versions of this question, but one question in the book is
asking to find all the polynomials of degree <= 2 whose graphs run through the points (1,1) and (2,0) such that integral (from 1 to 2) of f(t) dt = -1.

I have never done anything like this, so if anyone can help, thank you

2. Feb 9, 2008

### jhicks

Don't let the integral fool you! It's more of the same. What is the definite integral of $$ax^2+bx+c$$ from 1 to 2? Do the definite integral and you will see that you still have the same three unknowns.

3. Feb 9, 2008

### frasifrasi

ok, but at what point do I apply the integral?

4. Feb 9, 2008

### Dick

You have three conditions. Applying those conditions will still give you three linear equation in three unknowns. Compute the integral in terms of a,b and c.

5. Feb 10, 2008

### HallsofIvy

Staff Emeritus
Knowing that you can write the polynomial y= ax2+ bx+ c, what equation does x=1, y=1? x= 2, y= 0? x= 2, y= 0? And, of course, what equation, for a, b, and c, do you get from $$\int_1^2 (ax^2+ bx+ c)dx= -1$$?

6. Feb 10, 2008

### frasifrasi

I am doing the matrix for

a + b +c =1
and
4a + 2b + c =1

but het infinitely many solutions. Can you help me by saying if this is the correct matrix?

7. Feb 10, 2008

### Dick

You have a third equation. Work out the integral Halls was kind enough to write out.

8. Feb 10, 2008

### frasifrasi

I know this is a stupid question, but I am getting

7/3a + 3/2b + c = -1 for the integral. Can anyone confirm this? It is just the answer doesn't seem right.

9. Feb 10, 2008

### Dick

That's right.

10. Feb 10, 2008

### frasifrasi

Dick or anyone,

My book is terrible so I am having to research a lot of topics.

For the dot product of the col matrix
1
2
3

and

1
-2
1

I am getting
1
-4
3

just by multiplying, is this the correct way? how does this differ from matrix multiplication(cross product) once you are dealing with larger matrices?

11. Feb 10, 2008

### Dick

The dot product is the SUM of the products of the vector components. It's a scalar. In this case 1-4+3=0. If you work through matrix multiplication, you'll see you are building a matrix by taking dot products of row vectors and transposed column vectors.