Question: 1. Is the function below a linear transformation? Why or why not? (E)- 2. Determine the matrix representation of the linear transformation S below.

1. Is the function below a linear transformation? Why or why not? (E)- 2. Determine the matrix representation of the linear transformation S below. 3x1 +5x2 8x13x2 - 4x1 T: C C, T s:c+c, s([^]) = - 3x12 +3 8x2 - 6 3. Theorem LTLC has a fairly simple proof. Yet the result itself is very powerful. Comment on why we might say this. Theorem LTLC: Linear Transformations and Linear Combinations. Suppose that T: UV is a linear transformation, U, U2, U3,..., u are vectors from U and a, a2, a3,...,at are scalars from C. Then T(a + + + + ) = aT () + aT (1) + a3T (13) + + aT ()

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