Determine which of the following transformations are linear transformations.

A. The transformation T defined by T (x1, x2, x3) = (1, x2, x3)

B. The transformation T defined by T (x1, x2) = (2x1-3x2, x1+4,5x2).

C. The transformation T defined by T (x1, x2, x3) = (x1,0, x3)

D. The transformation T defined by T (x1, x2) = (4x1-2x2,3|x2|)

E. The transformation T defined by T (x1, x2, x3) = (x1, x2,-x3)

Question

Mathematics

Essence Forbes

14 May, 14:43

Determine which of the following transformations are linear transformations.

A. The transformation T defined by T (x1, x2, x3) = (1, x2, x3)

B. The transformation T defined by T (x1, x2) = (2x1-3x2, x1+4,5x2).

C. The transformation T defined by T (x1, x2, x3) = (x1,0, x3)

D. The transformation T defined by T (x1, x2) = (4x1-2x2,3|x2|)

E. The transformation T defined by T (x1, x2, x3) = (x1, x2,-x3)

+5

Answers (1)

Know the Answer?

Armani Ritter · Answer 1

The answer is letter C and E.

For A and B, they look like a linear transformation, however when you add the constants, it will not zero out. For letter D, it is not a linear transformation because of the scalar multiplication. The value given in D is an absolute value, so whether or not you multiply this, it will not result to the same number.