Question: Prove that the map T : R 3 >> R 3 defined by T ( < x 1 , x 2 , x 3 >)

Prove that the map T : R3 >> R3 defined by

T (< x1 , x2 , x3 >) = < 2x1 - 3x2 + 8x3 , 4x2 - x3 , 2x1 > is linear.

Find its standard matrix. Is T invertible? Explain how you know whether or not T is invertible.

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