Let V be the vector space of 2 × 2 real matrices and let P2...
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Let V be the vector space of 2 × 2 real matrices and let P2 bethe vector space of polynomials of degree less than or equal to 2.Write down a linear transformation T : V ? P2 with rank 2. You donot need to prove that the function you write down is a lineartransformation, but you may want to check this yourself. You do,however, need to prove that your transformation has rank 2.
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Let A a b c d be an arbitrary 2x2 matrix in V where a b c d are arbitrary real numbers Also let px ax2bx be an arbitrary polynomial in P2 Now let us define T V P2 by TA px Further let
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