Mathematics, 17.06.2020 04:57 donttrip10
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]
Answers: 2
![B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}](/tpl/images/0687/6238/93ed7.png)
![M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right]](/tpl/images/0687/6238/0cba0.png)
![A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right]](/tpl/images/0687/6238/feaec.png)
where a, b, c and d are real numbers![A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right]](/tpl/images/0687/6238/48850.png)
where 
![A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]](/tpl/images/0687/6238/dc48b.png)
![\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right]](/tpl/images/0687/6238/1f6e2.png)
and ![\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]](/tpl/images/0687/6238/84af8.png)
are apparently linearly independent and therefore form a basis B for V![M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right]](/tpl/images/0687/6238/77d7e.png)
can be written in the form ![M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]](/tpl/images/0687/6238/485b5.png)
![M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right]](/tpl/images/0687/6238/32f00.png)
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A square matrix AA is called half-magic if the sum of the numbers in each row and column is the same...
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