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MATH1231 Assignment 1z5362216November 2, 202111.1Question.The functionT:R2R3is defined byTx1x2=4x13x12x22x2for allx1x2R2Show thatTis a linear map
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22.1Question.Show that the setSgiven byS={xR4: 9x12x2+ 4x34x4= 0}is a subspace ofR42.2Solution.2.2.1Subspace theorem.A subset S of a vector space V over a fieldF, under the same rules for addition and multiplication byscalars, is a subspace of V if and only ifi) The vector0in V also belongs to S.ii) S is closed under vector addition, andiii) S is closed under multiplication by scalars fromF2.2.2Zero vector.As 9(0) - 2(0) + 4(0) - 4(0) = 0, the zero vector ofR4is in S. We now proceed to show the two closureaxioms.

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