Hi everybody!

I'm provided a table of values:

x: 0 1 2 3 4 5 6

y: 0 5 14 33 68 125 210

I used the Polynomial difference theorum to find that by subtracting consecutive y values to find the difference 3 times, they equalled out to 6's. So, I knew that it was degree 6, or ax^3 + bx+2 + cx + d.

So far so good.

Next, I'm instructed to use Matrices to find the coefficients. This is what's giving me trouble.

I set up the system:

T(4): 33 = 64a + 16b + 4c + d

T(3): 14 = 27a + 9b + 3c + d

T(2): 5 = 8a + 4b + 2c + d

T(1): 0 = 0a + 0b + 0c + 0d

Puting that into matrices, I have:

A: (4 by 4)

64, 16, 4, 1

27, 9, 3, 1

8, 4, 2, 1

0, 0, 0, 0

---

B: (4 by 1):

33,

14,

5,

0

When I multiply the inverse of matrix A times matrix B, I get an error message: "ERROR 03 SINGULAR MAT"

I know I can find the coefficients by using STAT, typing in the x values and the y values and using cubic regression, but I'm supposed to solve this using matrices. Any idea why this isn't working?

Thanks,

Ethan

Edit:

Sorry about the formatting, I had the data values spaced out nicely, but they clumped back together after I posted!