1) If A is 4×5 matrix with rank(A)=2 then the nullity of matrix A will be? Explain

2) If A is an 3×3 invertible matrix, then which statement is false? Explain
a)A has rank 3
b)nullity of A is 0
c)0 is an eigen value of A
d)det(A) is not equal to 0

3)Which of the following set of vectors form a basis for R^2 space? explain
a){(1, 4), (3, 12)}
b){(0, 5), (0, 3)}
c){(5, 2), (6, 0)}
d){(1, 0), (2, 0)}

4)Which of the following set of vectors is linearly independent?Explain
a){(1,0), (0,1)}
b){(0, 6), (0, 3)}
c){(1,0), (2,0)}
d){(1, 4), (3, 12)}

5) The statement “The set of vectors {v, kv} is linearly dependent for every scalar k.” is true or false?Explain