Weird Sum of Squares as a Vector Norm and Gauss-Newton optimization

[Sorento7]

Homework Statement

A(\vec{x}) = (F + T * x )²

F is a constant,
x is a 2×1 vector
T is a (constant) 1×2 matrixB(\vec{x}) = || K.Z.x ||² k:3\times3 matrix and Z:3\times2, x the same as aboveB(x) is also R²→RC(x) = A(x) + B(x)

Homework Equations

1- I am confused how can (A + B) be represented as a (vector) norm like this:

C(x) = || (F , 0) + (T , K).Z.x ||²

, i.e., what would be the dimensionality and meaning of the matrix (T , K) ? (discrepancy between the first 1 \times 2 entry and second 3 \times 3?)

The Attempt at a Solution

 

[Sorento7]

No solution?