Test series

Question

Comments

Can i use number of independent vector = n-r
n is number of variable and r is rank of matrix ??

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Here r is not the rank of A. It is the rank of (A-⋋I) where ⋋ is the eigen value.

No. of linearly independent eigen vectors = no. of distinct eigen values

The eigen values are 0,0,3. So answer should be 2. I don't know how they gave 3 :/

Can you please post the solution?

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Agreed with MINI

Statement said is correct.

https://math.stackexchange.com/questions/29371/how-to-prove-that-eigenvectors-from-different-eigenvalues-are-linearly-independe

BTW Don't trust ACE Test Series answers always.

Answer 1

answer is right it will 3

Comments

if we are find the eigen value then  these are 0,0,3

the linear independend vector for repeated eigen  valve is

first find the rank of the matrix for (A-⋋I) for  repeated like as 0 so let it suppose r them linear indepndent vector for this is n-r and and different eigen value give  separate independent eigen vector