True or False Give a brief justification for each answer Tru

True or False. Give a brief justification for each answer. True False The columns of a matrix A are linearly independent if Ax~ = 0~ has the trivial solution. True False Any 5 vector in R4 must be linearly dependent. True False Any 3 vector in R4 must be linearly independent. True False If AB = In, then B is the inverse of A.

Solution

1.
False, it may or may not have the trivial solution, i.e. zero vector.

2.
True, need 5 row pivots to make it linearly independent.

3.
False, 2 zero rows won