Linear Combinations: Definition & Equation


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Your generating set is {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. What would the linear combination of these elements be if you use the scalars 5, 7, and 0 in order?

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1. You are given (9, 2, 35, 8) from R4. Which of the following is NOT true about this element?

2. A grocery store receipt contains the following: 2 gallons of milk, 5 sticks of butter, and 3 quarts of vanilla yogurt. Which of the following statements accurately expresses this as a linear combination?

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About This Quiz & Worksheet

With this quiz and worksheet combination, you can find out what you know about linear combinations. Questions ask for the linear combination of a set of elements, and also, finding the combination for a generating set over a scalar set.

Quiz & Worksheet Goals

The quiz asks you about the following topics to test your understanding:

  • Characteristics of a given element
  • A linear combination involving a grocery store receipt
  • The meaning of 'linear combination'
  • The linear combination for a generating set over a scalar set

Skills Practiced

  • Information recall - remember what you have learned about generating sets and scalar sets
  • Problem solving - use what you know to solve practice problems, including one that uses a grocery store receipt
  • Defining key concepts - ensure that you can give a proper definition for linear combination

Additional Learning

For more about the material, check out the lesson titled Linear Combinations: Definition & Equation. By reviewing the lesson, you can view the additional material contained in this list:

  • Defining a generating set
  • The definition of a scalar
  • An example of a vector