In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation.
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Chapter 3 Solutions
Linear Algebra: A Modern Introduction
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- In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 9.arrow_forwardIn Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 10.arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 8. defined byarrow_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:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.arrow_forwardLet T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)arrow_forward
- In Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[x+zy+zx+y]arrow_forwardIn Exercises 3-6, prove that the given transformation is a linear transformation, using the definition (or the Remark following Example 3.55). 6.arrow_forwardIn Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[xy+z2x+y3z]arrow_forward
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