# Consider the linear transformation: M12 P1 from the set of 1 2 matrices to the set of polynomials of degree at most 1, defined by S ([a b]) = (3a + b) + (5a + 2b)x Prove that

Consider the linear transformation: M12 → P1 from the set of 1 × 2 matrices to the set of polynomials of degree at most 1, defined by

S ([a b]) = (3a + b) + (5a + 2b)x

Prove that S is invertible. Then show that the linear transformation

R: P1 → M12, R(r + sx) = [(2r - s) (-5r + 3s)]

is the inverse of S, that is S-1 = R.

S ([a b]) = (3a + b) + (5a + 2b)x

Prove that S is invertible. Then show that the linear transformation

R: P1 → M12, R(r + sx) = [(2r - s) (-5r + 3s)]

is the inverse of S, that is S-1 = R.

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## Determine the kernel of S first The condition that S a b 0 becomes 3a b 5a 2bx 0 …View the full answer

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