For problem 1-8, verify directly from Definition 6.1.3 that the given mapping is a linear transformation.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Differential Equations and Linear Algebra (4th Edition)
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardLet T be a linear transformation from R2 into R2 such that T(1,1)=(2,3) and T(0,2)=(0,8). Find T(2,4).arrow_forwardIn Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|arrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. 8. defined byarrow_forwardFind a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by T(A)=trt(A)arrow_forward
- [8] Find the inverse of the linear transformation T: R3 → R³ given by Ty y [x +arrow_forward1. (a) Use definition of linear transformation to determine whether the transformation T:R? → R³ defined as follows is linear. -y x+ 2y 2.x – 4y -arrow_forwardFor each of the following linear transformations T, determine whether Tis invertible and justify your answer. (a) T: R2 R3 defined by T(a1, a2) = (a12a2, a2, 3a1 + 4a2). (c) T: R3 R3 defined by T(a1, a2, a3) = (3a12a3, a2, 3a1 + 4a2). (d) T: P3(R) P2(R) defined by T(p(x)) = p'(x).arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,