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Consider the linear transformation
where
(a) Find
(b) Find
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Chapter 6 Solutions
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- Find 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_forwardFind the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardLet T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.arrow_forward
- Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardLet T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.arrow_forwardFind a basis for R2 that includes the vector (2,2).arrow_forward
- For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.arrow_forwardLet T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find T(1,4) and T(2,1).arrow_forwardLet T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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