A square matrix AA is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A)s(A) and is called the magic sum of the matrix AA. Let VV be the vector space of 2×22×2 half-magic squares. A) Find an ordered basis BB for VV.
B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

A)  

B)

Step-by-step explanation:

Let where a, b, c and d are real numbers

Since A is said to be a half magic square matrix, a = d, b = c.

The matrix A therefore becomes   where

A can therefore be manipulated as:

The matrices and are apparently linearly independent and therefore form a basis B for V

B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

can be written in the form

The coordinate vector is therefore,

the answer is -1 1/5, also a

hope i

-lavira : )