A binary classification task with input vectors bold x subscript n and targets t subscript n element of left curly bracket plus $1$ comma negative $1$ right curly bracket is perfectly achieved by a support vector machine classifier y with hat on top left parenthesis bold x right parenthesis equals w to the power of T bold f left parenthesis bold x right parenthesis plus b$,$ where bold f left parenthesis bold x right parenthesis are feature vectors. The weight vector that achieves this is bold italic w space equals space open parentheses table row cell $1$ divided by $2$ end cell row cell $1$ divided by $3$ end cell end table close parentheses. $(-6.,6.)$ and $(-3\mathrm{.}0,-4\mathrm{.}5)$ are support vectors.

Step by step explain the reason for your choice and Identify all the statements that are correct.

A$.$

$(-6.,6.)$ is a support vector belonging to class $+1$ and $(-3\mathrm{.}0,-4\mathrm{.}5)$ is a support vector belonging to class $-1.$

B$.$

$(-6.,6.)$ is a support vector belonging to class $-1$ and $(-3\mathrm{.}0,-4\mathrm{.}5)$ is a support vector belonging to class $+1.$

C$.$

The distance from either support vector to the decision boundary is $1\mathrm{.}66$

D$.$

A test point $(2,-7)$ is predicted to be in class $+1.$

E$.$

A test point $(2,-7)$ is predicted to be in class $-1.$

F$.$

The Euclidean distance between support vectors $(-6.,6.)$ and $(-3\mathrm{.}0,-4\mathrm{.}5)$ is greater than twice the distance of either point to the decision boundary