Which of the following is a linear transformation T R3R4 Whi

Which of the following is a linear transformation T: R^3--->R^4?

Which of the following is a linear transformationT:R3+R Hint first figure out the correct dimensions for the argument and the image. Second remember that each linear transformation might actually be defined by a matrix, therefore must have the form and the observation after (e) applies. A. T X1 +X2 x3 x3 x4 C, T xit 11 D. T

Solution

We need to determine which of the given options is a linear transformation from R³ to R⁴.

Since the transformation is from R3 to R4, therefore, argument of the tranformation must be in R³. In the given options, the arguments of options A and B are in R⁴. Therefore, options A and B get rejected.

Now, we need to look at options C and D. One of these must be the correct answer.

Option D is not actually a linear transformation because it is formed by NONHOMOGENEOUS system of linear equations. Therefore option D gets rejected too.

Lastly, option C is the correct option because it maps from R³ to R⁴ and it is system of HOMOGENOUS system of linear equations. Therefore, it forms the required linear transformation.