# Show that every plane through the origin in R3 may be identified with the null space of a vector in (R3)∗. State an analogous result for R2.

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Show that every plane through the origin in R3 may be identified with the null space of a vector in (R3)∗. State an analogous result for R2.

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Step 1

The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero.

It is the set of all the solution obtained from AB = 0, where A is known matrix and B is a matrix to be found.

Step 2

Any plane in R3 is of the form ax+by+cz=d, and if the plane passes through the origin it can be written in the form ax+by+cz=0, for some real numbers a,b,c.

Consider the vectors:

Step 3

The equation of the plane through origin ca...

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### Applications of Mathematics 