GATE Mathematics Practice Quiz

Question 1

Let T: R^5 -> R^3 be a linear transformation with rank(T)=2. What is nullity(T)?

Accepted Answer

3

Question 2

A 4 x 7 matrix A over R has rank 4. What is the dimension of the solution space of Ax=0?

Accepted Answer

3

Question 3

Let T: V -> V be a linear operator on a finite-dimensional vector space V with dim(V)=n. If rank(T^2)=rank(T), then which conclusion is necessarily true?

Accepted Answer

ker(T)=ker(T^2)

Question 4

Let T: R^6 -> R^6 satisfy dim(ker T)=2. What is the dimension of the solution space of T(x)=b for a vector b in Im(T)?

Accepted Answer

2

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