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# ZingPath: Inner Product and Linear Dependence

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## Inner Product and Linear Dependence

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### Lesson Focus

#### Standard Basis Vectors and Cartesian Coordinate Plane

Algebra-2

You will learn that any vector on the coordinate plane can be represented uniquely as a linear combination of the standard basis vectors.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Know the standard basis vectors for the coordinate plane.
• Know that all vectors on the plane can be represented uniquely through standard basis vectors.
• Write any vector in the plane as a linear combination of standard basis vectors given with coordinates.
• Determine any vector with coordinates, given as linear combination of standard basis vectors.

### Everything You'll Have Covered

Recall that vectors are quantities consisting of direction and magnitude. They are represented in the plane by directed line segments, and written algebraically using Cartesian coordinates.

To understand the concept of a basis, first consider a father who would like to communicate his position relative to his house. He might do so by telling his family how many miles east, west, north, or south he is from the house. We can view this situation using vectors.

The vector (1, 0) describes the position one mile east of his home. Similarly, one mile west is represented by (-1, 0), one mile north by (0, 1), and one mile west by (0, -1). No matter where the father is, he can communicate his position by using these vectors. For example, if he is five miles north and three miles west of the house, we could represent this by:

### Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts Students should know the Cartesian coordinate plane, and be familiar with vector addition and scalar multiplication of vectors. Course Algebra-2 Type of Tutorial Concept Development Key Vocabulary Displacement vector, linear combination, standard basis vectors