(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What choice of d would make matrix

a b

c d

have a rank of 1?

2. Relevant equations

rank(A) + nullity(A) = n

3. The attempt at a solution

In order for rank = 1, then nullity must = 1 because n = 2.

This isn't a nonsingular matrix, so det(A) = ad-bc =/= 0.

d = bc/a, where 'a' cannot be 0.

Let's say a = 1, then the matrix will be

1 ad/c

c d

c cannot be 0 either, so matrix is now

1 d

1 d

and I guess a possible candidate would just then be

1 1

1 1?

I think I'm supposed to give the answer in more arbitrary terms, so I am lost here.

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# Homework Help: Choice of variable to make matrix rank = 1

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