Suppose v1, v2 and v3 are vectors in R 3 such that 4v1 + 3v2 − v3 = 0 Which of the following statements must be TRUE? (I) v3 ∈ span{v1, v2} (II) det   v1 v2 v3   = 0 (III) If W = span{v1, v2, v3}, then the dimension of W is at most 2.

  7

 ————

 15x2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (4 • (x2))      7y  

 —————————— • ————————

     5y       (22•3x4)

Step  2  :

              7y  

Simplify   ————————

           (22•3x4)

Equation at the end of step  2  :

 (4 • (x2))    7y

 —————————— • ————

     5y       12x4

Step  3  :

Equation at the end of step  3  :

 22x2    7y

 ———— • ————

  5y    12x4

Step  4  :

           22x2

Simplify   ————

            5y

Equation at the end of step  4  :

 4x2    7y

 ——— • ————

 5y    12x4

Step  5  :

Dividing exponential expressions :

5.1    x2 divided by x4 = x(2 - 4) = x(-2) = 1/x2

Canceling Out :

5.2    Canceling out y as it appears on both sides of the fraction line

Final result :

   7

 ————

 15x2

Step-by-step explanation: