Find the dimension of the subspace of all vectors in set of real numbers r superscript 4ℝ4 whose firstfirst and thirdthird entries are equal.

The subspace has dimension 3.

Intuitively, you can think that you're removing one degree of freedom from . In fact, this space is generated by the following span:

Since the first and third coordinate must be the same, we have . So, the span becomes

which is the same as

And so you can see that the space is generated by three vectors.

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

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step-by-step explanation: