Hi so I'm doing some SAT practice and I'm quite lost
One of the questions says for all integers x, y, z let (x, y, z)*shaded triangle* be defined by (x, y,z)*shaded triangle*= xsq, ysq, z,sq. Then it gives me (1,2,3)*shadedtriangle*/(3,2,1)*shaded triangle*. I can't figure out what the shaded triangle stands for, what do do with the bracket in the equation. Very lost. Help!
No idea what xsq is. x^2?
And what is the triple "xsq, ysq, z,sq" supposed to mean?
I'll use © for the operator.
You say
(x,y,z)© = xsq, ysq, z,sq
I have no idea what that means. Is it x^2+y^2+z^2?
Gotta help me out here.
The symbol "*shaded triangle*" represents a mathematical operation called the "Hadamard product" or "element-wise multiplication." It is a way to multiply two vectors or matrices of the same dimensions, where each corresponding element in the two vectors or matrices is multiplied together.
In the given question, (x, y, z)*shaded triangle* refers to element-wise multiplication of the three values (x, y, z) with themselves, resulting in (x^2, y^2, z^2).
Now, let's tackle the expression (1,2,3)*shaded triangle*/(3,2,1)*shaded triangle*.
To perform this operation, we need to find the element-wise multiplication of (1, 2, 3) and (3, 2, 1):
(1, 2, 3) *shaded triangle* (3, 2, 1) = (1*3, 2*2, 3*1) = (3, 4, 3).
So, (1, 2, 3)*shaded triangle*/(3, 2, 1)*shaded triangle* = (3, 4, 3)/(3, 2, 1).
To compute (3, 4, 3)/(3, 2, 1), we need to divide each corresponding element of (3, 4, 3) by the corresponding element of (3, 2, 1):
(3, 4, 3)/(3, 2, 1) = (3/3, 4/2, 3/1) = (1, 2, 3).
Therefore, (1, 2, 3)*shaded triangle*/(3, 2, 1)*shaded triangle* simplifies to (1, 2, 3).