MTH 141 Chapter Notes - Chapter 1: Parametric Equation, Scalar Multiplication, Parallelepiped

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fuchsiatermite554

1 Jan 2016

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Document Summary

Standard basis any vector can be written as a sum of scalar multiples of e1 and e2. Proving a set is not in the subspace. Be in the zero subspace (trivial subspace) If a set is in the subspace = the set is called a spanning set for the subspace. Linearly dependent one of the vectors is equal to a linear combination of some of the other vectors. We can find the other vectors where there are solutions that are non-zero. Has a solution thus it is linearly dependent. Linearly independent the only solution to the equation must be 0. Basis v is a spanning set for subspace of s of r^n , v is linearly independent. Plane (linearly independent) v1, v2 and passes through p. Dot product/ scalar product / standard inner product. Scalar equation of planes/hyperplanes (sub in point into x1,x2,x3) Need a point, and normal vector, finding x1,x2,x3 ( a point on the plane)

Related Questions

Same line: Different Parametric Equation Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equations. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations:

Line 1:

Line 2:

(a) Find two points that lie on Line 1 by setting and in its parametric equations. Then show that these points also lie on Line 2 by finding two values of the parameter that give these points when substituted into the parametric equations for Line 2.

yellowchimpanzee154

Discuss: Same Line; Different Parametric Equations; Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equation. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations;

Show that the following two lines are not the same by finding a point on Line and then showing that is does not lie on Line .

lilactiger364

DISCUSS(same Line):

Different Parametric Equations Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equations. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations:

(a) Find two points that lie on Line 1 by setting and in its parametric equations. Then show that these points also lie on by finding two values of the parameter that give these points when substituted into the parametric equations for .