Which of the following linear transformations from R3 to R3

Which of the following linear transformations from R^3 to R^3 are invertible? Projection onto the yz- plane Identity transformation (i.e. T(v) = v for all v) Reflection in the xy- plane Projection into the x- axis Reflection in the origin Rotation about the z-axis Trivial transformation (i.e. T(v) = 0 for all v) Dilation by a factor of 3

Solution

from the given transformations 2, 3, 6, 8 are invertable

and remaining 1,4,5,7 are not

 Which of the following linear transformations from R^3 to R^3 are invertible? Projection onto the yz- plane Identity transformation (i.e. T(v) = v for all v) R

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