1st column of P+Q is linear combination of 2nd and 3rd column as col1=2*col2-col3. So rank cannot be 3
Anyone who tried to solve usingRank(A+B) = Rank(A)+Rank(B) and got answer as 3, the problem is it is not an equality equation.The equation is:Rank(A+B) ≤ Rank(A)+Rank(B)
and 2 is clearly less than 3
1st and 2nd
or
3rd and 2nd
Rank of matrix tells about a lot of things :-
One thing to note is that
number of linear independent rows are equal to number of linear independent columns.
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