MAT188H1 Midterm: MAT188H1_20169_641483478520mat188tut5sol
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MAT188H1 Full Course Notes
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Faculty of applied science & engineering, university of toronto. Tutorial problems 5: consider the subset of r4. | a, b, c r) (a) show that w is a subspace of r4. Hint: the easiest way to do this is to show w is the span of some vectors in r4 (c. f. This will also help you answer part (b) below. 2a + b + 3c a + b + 2c a + 2b + 3c. W =(av1 + bv2 + cv3 | a, b, c r) | a, b, c r) (1) (2) (3) where v1 = . Therefore, for any vector x w , we have x = av1 + bv2 + cv3, for some a, b, c r, so that w = span{v1, v2, v3}. Using theorem 2, page 18, it follows that w is a subspace of r4. (b) find a basis for w . In part (a), we have proved that w = span{v1, v2, v3}.
