Suppose the linear function T : R 3 ->R 2 is onto. Select all the true statement

ID: 3196176 • Letter: S

Question

Suppose the linear function T : R3->R2 is onto. Select all the true statements from the list below.

- Ever in R2 is an image of some element in R3 under T.

- T(a) = T(b) implies a=b

There is a unique element a in R3 such that T(a) = 0

There must be some element a in R3 for which T(a ) = (123,456).

For every b in R2, there is some a in R3 such that T(a ) = b.

-There is no element a in R3 such that T(a) = 0

- Ever in R2 is an image of some element in R3 under T.

- T(a) = T(b) implies a=b

There is a unique element a in R3 such that T(a) = 0

There must be some element a in R3 for which T(a ) = (123,456).

For every b in R2, there is some a in R3 such that T(a ) = b.

-There is no element a in R3 such that T(a) = 0

Statements 1,2,3,4,5 are all true. Statement 6 is not true.

(statement 1 is not properly written. it should be - every element in R^2 is an image of some element in R^3 under T.)

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