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T:R3 rightarrow R3. and T(( x1, x2, x3)) = (3x1, - 6x2 + x3, -x1 + 2x2 - 5x3, x1

ID: 3084592 • Letter: T

Question

T:R3 rightarrow R3. and T(( x1, x2, x3)) = (3x1, - 6x2 + x3, -x1 + 2x2 - 5x3, x1, - 2x2, - 9x3) Find the Range of T. and write it with an appropriate notation Find the Kernel of T. and write it with an appropriate notation. Find the preimage of ( 4. -7.0 ). if it exists, and write it with an appropriate notation Repeat part (c). but with ( 17. -29. -41 ). Find the rank and nullity of T. Is T a one-to-one transformation? Why, or why not? Is T an onto transformation? Why.,or why not? Is T a one-to-one correspondence? Why or why not?

Explanation / Answer

dimension of range is 2 and dimension of kernel is 1 t is 1 -1 and onto

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T:R3 rightarrow R3. and T(( x1, x2, x3)) = (3x1, - 6x2 + x3, -x1 + 2x2 - 5x3, x1

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