Define a linear transformation T : R? → R37: R - R' by T(a1, x2) = (3xı + a2, 5a1 + 7x2, 2a1 + 3x2) Find a matrix representation for T. If you are not sure about your answer, at least state the size of the matrix.

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Let the transformation T : IR³ →R² be given by the formula T(x,,X2,X3) = (2x, –x,, X, +3x;). Find the standard matrix of this transformation and write it in matrix multiplication form. Check correctness of your answer for the point (1,4,-3).

Assume that T is a linear transformation and T(1,2,1)=(2,1,3), T(-1,2,3)=(1,1,3), 7(2,1,3)=(1,-1,3), Find the image of (2, 1, 2) under T. Give the components of the answer a₁, a2, a3 as in the ordered triple (a₁, a₂, a3). Using Fractions in simplest form and NO DECIMALS "a₁= "),a2= a3=