Kenneth Kuttler

180 CHAPTER 8. RANK OF A MATRIX

23. Here are three vectors. Determine whether they are linearly independent or linearlydependent. (

1 2 0)T

2 0 1)T

3 0 0)T

24. Here are three vectors. Determine whether they are linearly independent or linearlydependent. (

4 2 0)T

2 2 1)T

0 2 2)T

25. Here are three vectors. Determine whether they are linearly independent or linearlydependent. (

1 2 3)T

4 5 1)T

3 1 0)T

26. Here are four vectors. Determine whether they span R3. Are these vectors linearlyindependent?(

1 2 3)T

4 3 3)T

3 1 0)T

2 4 6)T

27. Here are four vectors. Determine whether they span R3. Are these vectors linearlyindependent?(

1 2 3)T

4 3 3)T

3 2 0)T

2 4 6)T

28. Determine whether the following vectors are a basis for R3. If they are, explain whythey are and if they are not, give a reason and tell whether they span R3.(

1 0 3)T

4 3 3)T

1 2 0)T

2 4 0)T

29. Determine whether the following vectors are a basis for R3. If they are, explain whythey are and if they are not, give a reason and tell whether they span R3.(

1 0 3)T

0 1 0)T

1 2 0)T

30. Determine whether the following vectors are a basis for R3. If they are, explain whythey are and if they are not, give a reason and tell whether they span R3.(

1 0 3)T

0 1 0)T

1 2 0)T

0 0 0)T

31. Determine whether the following vectors are a basis for R3. If they are, explain whythey are and if they are not, give a reason and tell whether they span R3.(

1 0 3)T

0 1 0)T

1 1 3)T

0 0 0)T

18023.24.25.26.27.28.29.30.31.CHAPTER 8. RANK OF A MATRIXHere are three vectors. Determine whether they are linearly independent or linearlydependent.T T T(1 2 0) (2 0 1) .(3 0 0 )Here are three vectors. Determine whether they are linearly independent or linearlydependent.T T T(4 2 0) (2 2 1) ,(0 2 2 )Here are three vectors. Determine whether they are linearly independent or linearlydependent.(1 2 3)'.(4 5 1)'.(3 1 0)"Here are four vectors. Determine whether they span R?. Are these vectors linearlyindependent?(1 2 3)(4 3 3)'.(3 1 0) (2 4 6)Here are four vectors. Determine whether they span R?. Are these vectors linearlyindependent?(1 2 3)(4 3 3)'.(3 2 0) (2 4 6)Determine whether the following vectors are a basis for R*. If they are, explain whythey are and if they are not, give a reason and tell whether they span R?.(1 0 3)'.(4 3 3)(1 2 0) (2 4 0)"Determine whether the following vectors are a basis for R*. If they are, explain whythey are and if they are not, give a reason and tell whether they span R?.(1 0 3)'.(0 1 0).(1 2 0)"Determine whether the following vectors are a basis for R*. If they are, explain whythey are and if they are not, give a reason and tell whether they span R?.(1 0 3)'.(0 1 0) (1 2 0)'.(0 0 0)"Determine whether the following vectors are a basis for R*. If they are, explain whythey are and if they are not, give a reason and tell whether they span R?.(1 0 3)'.(0 1 0)'.(1 1 3)'.(0 0 0)"