I'm struggling with this exercise:
Find the possible ranks of the matrix D, depending on the values of a and b.
Da,b=⎣⎢⎢⎢⎡a010−11011a21b12a⎦⎥⎥⎥⎤
After reducing D to row echelon form I got:
⎣⎢⎢⎢⎡100001002a1−a021b−2a+1b−a⎦⎥⎥⎥⎤
Based on this I concluded that if a=1 and b=1 then r(D)=2; If a=b and a,b=1 then r(D)=3.
Apparently this is incorrect according to the solutions in the book, and I can't really understand why.
Find the possible ranks of the matrix D, depending on the values of a and b.
Da,b=⎣⎢⎢⎢⎡a010−11011a21b12a⎦⎥⎥⎥⎤
After reducing D to row echelon form I got:
⎣⎢⎢⎢⎡100001002a1−a021b−2a+1b−a⎦⎥⎥⎥⎤
Based on this I concluded that if a=1 and b=1 then r(D)=2; If a=b and a,b=1 then r(D)=3.
Apparently this is incorrect according to the solutions in the book, and I can't really understand why.
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