We have the given matrix M such that M = [4 5 p 5 4 q 0 5 r] We know that the two vectors (4, 5, 0) and (5, 4, 5) span a plane in R^3 such that the two vectors are linearly independent of each other. What should the conditions in the third vector be if we want the three vectors to span R^3?

We have the given matrix M such that M = [4 5 p 5 4 q 0 5 r] We know that the two vectors (4, 5, 0) and (5, 4, 5) span a plane in R^3 such that the two vectors are linearly independent of each other. What should the conditions in the third vector be if we want the three vectors to span R^3?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

We have the given matrix M such that

M = [4 5 p

5 4 q

0 5 r]

We know that the two vectors (4, 5, 0) and (5, 4, 5) span a plane in R^3 such that the two vectors are linearly independent of each other. What should the conditions in the third vector be if we want the three vectors to span R^3?

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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