Question

show that matrix

1 x x^2
1 y y^2
1 z z^2

is (y-x)(z-x)(z-y)

Answer 1

do you mean the determinant is (y-x)(z-x)(z-y)? That is a Vandermonde matrix, and its determinant is well known to be what you posted. If i had to show that was the determinant, I would row reduce the matrix to make the bottom two 1's in the first column 0, then get the determinant.

Answer 2

i like your pi t shirt

Answer 3

thanks :)

Answer 4

the question didnt ask anything about the determinant but ill give it a try

Answer 5

hmmm, i wonder what the question meant then =/

Answer 6

the question is underspecified otherwise; did the problem explain how you're supposed to reduce a 3x3 matrix into a single expression? otherwise it's like asking "show that red, green, blue is equal to 49"

Answer 7

here ya go :)

Answer 8

nope ='[ what i typed is exactly what the question is lol

Answer 9

its gotta be the determinant. That type of matrix is special, and really well known about. basically, if you have an n x n Vandermonde matrix, you can tell if its invertible or not just by looking at it.

Answer 10

matrix is just an arrangement so we cannot find the value of it.......??