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1.3 Vector Equations

1.3 Vector Equations. : 1-column matrices or ordered pairs of real numbers. Vectors in R 2. Example : Given and , find. Geometric Interpretation?. : column matrices or points in three-dimensional space. Vectors in R 3.

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1.3 Vector Equations

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  1. 1.3 Vector Equations

  2. : 1-column matrices or ordered pairs of real numbers Vectors in R2 Example: Given and , find Geometric Interpretation?

  3. : column matrices or points in three-dimensional space Vectors in R3 Vectors in Rn : column matrices

  4. Two vectors are equal if and only if their corresponding entries are equal. • The vector (where c is a real number) is a scalar multiple of .

  5. Algebraic Properties of

  6. Linear Combinations Given vectors and given scalars is a linear combination of with weights Example:

  7. Example: Determine whether w can be generated as a linear Combination of v and v , where , , and .

  8. A vector equation has the same solution set as the linear system whose augmented matrix is can be generated by a linear combination of vectors in if and only if the following linear system is consistent:

  9. Definition If , then the set of all linear combinations of is denoted by Span and is called the subset of spanned by

  10. Geometric Description of Span:

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