Solution Found!
a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the
Chapter 2, Problem 11(choose chapter or problem)
a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the function cT : Rn Rm defined by (cT )(x) = cT (x) (i.e., the scalar c times the vector T (x)) is also a linear transformation. b. Prove that if S : Rn Rm and T : Rn Rm are linear transformations, then the function S + T : Rn Rm defined by (S + T )(x) = S(x) + T (x) is also a linear transformation. c. Prove that if S : Rm Rp and T : Rn Rm are linear transformations, then the function ST : Rn Rp is also a linear transformation.
Questions & Answers
QUESTION:
a. Prove that if T : Rn Rm is a linear transformation and c is any scalar, then the function cT : Rn Rm defined by (cT )(x) = cT (x) (i.e., the scalar c times the vector T (x)) is also a linear transformation. b. Prove that if S : Rn Rm and T : Rn Rm are linear transformations, then the function S + T : Rn Rm defined by (S + T )(x) = S(x) + T (x) is also a linear transformation. c. Prove that if S : Rm Rp and T : Rn Rm are linear transformations, then the function ST : Rn Rp is also a linear transformation.
ANSWER:Problem 11
a. Prove that if 
b. Prove that if 
c. Prove that if 
Step-by-step solution
Step 1 of 3
a)
Given
Defined by 
i)
Also
ii)
Also
Hence 