Suppose that T is a matrix transformation such that T : R R, and we...

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Suppose that T is a matrix transformation such that T : R² → R³, and we know that -1 1 3 2 2 TH)-470) - T(2₁) = and T(7₂) = -1 where ₁ and 2 are the columns of the 2 × 2 identity matrix. (a) Find the matrix A such that T(x) = Ax and hence determine T(v) for v = 3 - [ ] 19 6 (b) Determine and describe all vectors such that T(x) = -3 4 (c) True or false: for any b in R³, we can find a solution ☞ to the equation T(x) = b. (Be sure to justify your conclusion.) Suppose that T is a matrix transformation such that T : R² → R³, and we know that -1 1 3 2 2 TH)-470) - T(2₁) = and T(7₂) = -1 where ₁ and 2 are the columns of the 2 × 2 identity matrix. (a) Find the matrix A such that T(x) = Ax and hence determine T(v) for v = 3 - [ ] 19 6 (b) Determine and describe all vectors such that T(x) = -3 4 (c) True or false: for any b in R³, we can find a solution ☞ to the equation T(x) = b. (Be sure to justify your conclusion.)

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