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Forming a Basis in R4

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Find a basis for each of the following subspaces of R4.

a) Find all vectors that satisfy the equation x1 - 3x2 + 6x3 - 4x4 = 0.

b) Find all vectors whose entries satisfy both equations x1 + x2 + x3 + x4 = 0 and x1 - x3 = 0.

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Solution Summary

This solution shows how to find vectors that satisfy certain equations.

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a) Since there is only one equation in the question, there are infinite possibilities of making a basis that satisfies the equation:

we only need to plug the easiest values that satisfy the ...

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