Question

1. Let a,b,c,d be row vectors and form the matrix A whose rows are a,b,c,d. If by a sequence of row operations applied to A we reach a matrix whose last row is 0 (all entries are 0) then:
      
a. a,b,c,d are linearly dependent  
b. one of a,b,c,d must be 0.      
c. {a,b,c,d} is linearly independent.      
d. {a,b,c,d} is a basis.

2. Suppose a, b, c, d are vectors in R4 . Then they form a basis of R4 if
  
a. the matrix whose columns are a,b,c,d has non-zero determinant.
b. the matrix whose columns are a,b,c,d has zero determinant.  
c. if a+b=c+d      
d. one of the vectors a,b,c,d is 0.

Answer 1