The linear combinations of v = (a,b) and w = (c,d) fill the planes unless _______. Find four vectors u,v,w,z with four components of each so that their combinations cu+dv+ew+fz produce all vectors ( b1,b2,b3,b4) in four dimensional space.

The linear combinations of v = (a,b) and w = (c,d) fill the planes unless _______. Find four vectors u,v,w,z with four components of each so that their combinations cu+dv+ew+fz produce all vectors ( b1,b2,b3,b4) in four dimensional space.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 72E: Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear...

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

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Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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