Section 1.8 Problem 5. Mark each statement True or False, and justify your answer. (T/F) A linear transformation is a special type of function. (T/F) Every matrix transformation is a linear transformation. (T/F) If A is a 3x5 matrix and T is a transformation defined by T(x)=Ax, then the domain of T is R³. (T/F) The codomain of the transformation x-Ax is the set of all linear combinations of the columns of A. (T/F) If A is an mxn matrix, then the range of the transformation x-Axis R". (T/F) If T:R+R is a linear transformation and if c is in R", then a uniqueness question is "Is c in the range of T?" (T/F) A linear transformation preserves the operations of vector addition and scalar multiplication. (T/F) A transformation T is linear if and only if T(ov+c₂v)T(v₁)+c₂T(v₂) for all v₁ and v₂ in the domain of T and for all scalars c₁ and c (T/F) The superposition principle is a physical description of a linear transformation.

Q: F:R³ → R² defined by ED- 3x1 + x2 - 6x3] -X1 + x2 + 13x3] F

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