Question

Asked Dec 28, 2019

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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.

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 R^{3} 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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