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.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

529 and 531

step-by-step explanation: