(question corrected) if A = [5000;0500;0050;0005] - [1111;1111;1111;1111], and A
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(question corrected) if A = [5000;0500;0050;0005] - [1111;1111;1111;1111], and A^-1 = [2/5 1/5 1/5 1/5; 1/5 2/5 1/5 1/5; 1/5 1/5 2/5 1/5; 1/5 1/5 1/5 2/5], then what will be "k" and "h" in A_2 = [k000;0k00;00k0;000k] + [hhhh;hhhh;hhhh;hhhh] which makes inverse of A_2 = inverse A? (it means subtraction with k=5,h=1 and addition k=?,h=? makes same inverse. so need to find k&h; for addition) Also what will be "k" and "h" in 5*5 matrix B = [70000;07000;00700;00070;00007] - [11111;11111;11111;11111;11111], B^-1 = [3/14 1/14 1/14 1/14 1/14; 1/14 3/14 1/14.....]?Explanation / Answer
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Matrix A is:
4 -1 -1 -1
-1 4 -1 -1
-1 -1 4 -1
-1 -1 -1 4
Inverse Matrix A we get by the above=
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
But we have it as A-1;
A^-1 = [2/5 1/5 1/5 1/5; 1/5 2/5 1/5 1/5; 1/5 1/5 2/5 1/5; 1/5 1/5 1/5 2/5]
Which satisfy the values k=5 & h=1;
In Matrix A_2 = [k000;0k00;00k0;000k] + [hhhh;hhhh;hhhh;hhhh]
Value of K & h be k=5, h=1 satisfy the given condition.
b)
The same way:
B^-1 = [3/14 1/14 1/14 1/14 1/14; 1/14 3/14 1/14.....]
k=14 & h=3 satisfys it
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