Find a basis for the set of vectors in set of real numbers R cubed in the plane x minus 7 y plus 4 z equals 0. [Hint: Think of the equation as a "system" of homogeneous equations.] A basis for the set of vectors in set of real numbers R cubed in the plane x minus 7 y plus 4 z equals 0 is StartSet nothing EndSet .

Step-by-step explanation:

Any vector in this plane is actually a solution to the homogeneous system x-7y+4z = 0 (although this system contains only one equation). So we are to find a basis for the kernel of the coefficient matrix

A = x-7y+4z = 0

A =(1, -7, 4)

let x = 7y - 4z

  =

∴  form a basis for kernel A

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above