21.7.2. Use in Engineering

Try these first

1. 1.

   Define linear dependence.

   Hint

   Think of whether one vector can be formed with the others.

2. 2.

   What is linear independence?

   Hint

   Remember, the scalars must all be zero.

3. 3.

   What defines linear dependence?

   • A vector can stand alone.
   • One vector can be expressed as a combination of others.
   • All vectors are independent.

   Hint

   Think about how vectors relate to each other.

4. 4.

   True or False: The vector set { (1, 2), (2, 4) } is linearly independent.

   • True
   • False

   Hint

   Check if one vector can be made by combining others.

5. 5.

   Consider the vectors v1 = (1, 2, 3), v2 = (2, 4, 6), and v3 = (3, 6, 9). Are these vectors linearly dependent or independent? Justify your answer.

   Hint

   Look for constants that can express one vector through another.

6. 6.

   An engineer decides to remove redundant structural supports based on vector analysis. If the original supports were based on vectors that are dependent, how would this affect the safety of the structure?

   Hint

   Re-evaluate the role each support plays in load-bearing.