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12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing

Let L : R2 → R3 be a linear transformation such that L 1 1 = 1 2 3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix representing L. Find the dimensions of the kernel and the range of L and their bases.

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Given that, 1.12² m3 is given by To find L(²), net ,, l th such that a(1) +62 ()-(?) i citl= 22 = 2 =21 +2 = 1 e, 23 - 10%)-1[2] 31 ur The Standard marrin for L will be 10 ( 30 ) there are two linearing independent column are there. here, dim (range

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