Please solve all

15) Find a basis for Col B where 15) 0 O -2 0 BE O O 0 O 0 O -1 + N 16) Let A = WN - - 2 -7 - 3 16) -6 - 9 -11 OUON O It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. 17) Let v1 = 17) Note that v3 = 2v1 - 3v2. Which of the following sets form a basis for the subspace H, i.e., which sets form an efficient spanning set containing no unnecessary vectors? Option 1: (V1. V2. V3} Option 2: (v1, V2} Option 3: {V1, V3} Option 4: (v2, V3 } Determine whether the set of vectors is a basis for R. 18) Given the set of vectors . o . 1 , decide which of the following statements is true. 18) Option 1: Set is linearly independent and spans . Set is a basis for A3. Option 2: Set is linearly independent but does not span . Set is not a basis for 13. Option 3: Set spans & but is not linearly independent. Set is not a basis for R. Option 4: Set is not linearly independent and does not span . Set is not a basis for R. decide which of the following statements is 19) true: Option 1: Set is linearly independent and spans . Set is a basis for R. Option 2: Set is linearly independent but does not span . Set is not a basis for 13. Option 3: Set spans & but is not linearly independent. Set is not a basis for R. Option 4: Set is not linearly independent and does not span R. Set is not a basis for $3. 20) 8 - { 29 18= . Find the vector x determined by the given coordinate 20) vector [x] B and the given basis B