(2) Decide whether the following sets are vector spaces over the field of real numbers. (a) The set of complex numbers. (b) The set of complex valued functions on ? such that f(x) ? 0 for every x ? ?. (c) The set of 2 × 2 matrices with rational entries. (d) The set of 2 × 2 invertible matrices with real entries. You may simply write "True" or "False". No justification is required.
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The following are vector spaces over the field of rational numbers. Compute their dimension over Q. (a) The set of rational numbers. (b) The set of 2 x 2 matrices with rational entries. (c) The set of 2 x 2 matrices with real entries. (d) The set of functions from R to Q.
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