Solve and show work. Determine whether the linear transformation T is one-to-one

Question

Solve and show work.

Determine whether the linear transformation T is one-to-one and whether it maps as specified.

Choose the best answer from the options below

Determine whether the linear transformation T is one-to-one and whether it maps as specified. Determine whether the linear transformation T is one-to-one and whether it maps as specified. Determine whether the linear transformation T is one-to-one and whether it maps 3 onto 3. Choose the best answer from the options below One-to-one; not onto 3 One-to-one; onto 3 Not one-to-one; onto 3 Not one-to-one; not onto 3

Explanation / Answer

T(x) = Ax

matrix A is

1 -2 3

-1 3 -4

7 4 -5

R2 to R2+R1

R3 to R3+7R2

new matrix is

1 -2 3

0 1 -1

0 25 -33

we can see that rank of matrix A is 3

So it is on to one and it is onto because it will map to all values .

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