I need help with these question thanks

QUESTION 1:

Construct 3 x2 matrices A and B such that Ax = 0 has only one trivial solution and Bx = 0 has a nontrivial solution. llBIQSL l l Insert Formula Suppose A is an m x n matrix with the property that for all b in R" the equation Ax = b has at most one solution. Use the definition of linear independence to explain why the columns of A must be linearly independent. B I U SIX E Insert FormulaSuppose an m x n matrix A has n pivot columns. Explain why for each h in [Him the equation Ax = b has at most one solution. [Hint: Explain why Ax = b cannot have innitely many solutions.] 'H'BIQSIE Insert Formula