Matrix Algebra

[abstract yoke]

I had a question on this problem. Can anyone tell me on how to approach and solve this question? Do i make a matrix and then do gaussian elimination on it? How would I set up the matrix(what would it look like)

[vivid lily]

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[visual moth]

In general, n points can be interpolated using a (n - 1)th degree polynomial. So, in this case, cubic:
y = ax^3 + bx^2 + cx + d
We know that, for example, y(2) = -2. That gives an equation:
-8a + 4b - 2c + d = 2
Using the other three points, you get three more equations. Then you just solve the system as usual.

[abstract yoke]

shouldnt it be 8a + 4b - 2c + d = -2?

[visual moth]

Oh, sorry, my bad, mixed it up. Of course.

[jovial mica]

you can also use Lagrange polynomials

[visual moth]

Yes, but this exercise asks for Gauss's method to be used.

[jovial mica]

i know. im just saying that OP can use that in case they get a problem like this without using gaussian elimination