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Let M be a 7 6 real matrix. The entries of M in the position ( 1 , 3 ) , ( 1 , 4

Let

M

be a

7 6

real matrix. The entries of

M

in the position

(1, 3), (1, 4), (3, 3), (3, 4)

and

(5, 4)

are changed to obtain another

7 6

real matrix tilde

(M) .

Suppose that the rank of tilde

(M)

4 .

What is the sum of all possibilities of rank of

M ?

Answer:

147

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