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# Maths matrices question! Help!! watch

1. A magic (square) matrix is an n x n matrix, whose rows and columns, and whose two main diagonals, sum to the same number.

Suppose A, a 3 × 3 magic matrix with entries aij , has row sum r. Explain why
this is equivalent to the linear equations Mv = 0 where v is the column vector
that is the transpose of (r, a11, a12, a13, a21, a22, a23, a31, a32, a33) and M is the
8 × 10 matrix:

M =

(−1 1 1 1 0 0 0 0 0 0)
(−1 0 0 0 1 1 1 0 0 0)
(−1 0 0 0 0 0 0 1 1 1)
(−1 1 0 0 1 0 0 1 0 0)
(−1 0 1 0 0 1 0 0 1 0)
(−1 0 0 1 0 0 1 0 0 1)
(−1 1 0 0 0 1 0 0 0 1)
(−1 0 0 1 0 1 0 1 0 0)

Repeat for 4 x 4 magic squares.
2. Hey I've moved this from maths uni courses to maths study help.
3. (Original post by cecfm29)
A magic (square) matrix is an n x n matrix, whose rows and columns, and whose two main diagonals, sum to the same number.

Suppose A, a 3 × 3 magic matrix with entries aij , has row sum r. Explain why
this is equivalent to the linear equations Mv = 0 where v is the column vector
that is the transpose of (r, a11, a12, a13, a21, a22, a23, a31, a32, a33) and M is the
8 × 10 matrix:

M =

(−1 1 1 1 0 0 0 0 0 0)
(−1 0 0 0 1 1 1 0 0 0)
(−1 0 0 0 0 0 0 1 1 1)
(−1 1 0 0 1 0 0 1 0 0)
(−1 0 1 0 0 1 0 0 1 0)
(−1 0 0 1 0 0 1 0 0 1)
(−1 1 0 0 0 1 0 0 0 1)
(−1 0 0 1 0 1 0 1 0 0)

Repeat for 4 x 4 magic squares.
Zacken TeeEm Student403
4. Zacken will get this I'm sure
5. (Original post by Student403)
Zacken will get this I'm sure
lol
6. What do you mean by a matrix is equivalent to an equation? Do you mean that the restrictions on the matrix are equivalent to the equation? If so, go through each one by one and see if they're in the set of equations.

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