Question: (12 marks) 14. Consider the transformation T:R? - R?, such that every vector * = (x1, x2,X3 ) ER is mapped to R2 in the

(12 marks) 14. Consider the transformation T:R? - R?, such that every vector * = (x1, x2,X3 ) ER is mapped to R2 in the following manner: T: (X1, X2, X3) - (x; 5x2 + 4x3, x2 - 6x3). (a) Show that t is a linear transformation (b) Find the standard matrix of T. (c) Find the range of T and establish whether T is onto R (d) Is T an one-to-one transformation on its range? Explain

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