In Exercises 25-28, determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer.
27. The transformation in Exercise 19
In Exercises 17-20, show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2,... are not
19. T(x1, x2, x3) = (x1 − 5x2 + 4x3, x2 – 6x3)
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Chapter 1 Solutions
Linear Algebra and Its Applications (5th Edition)
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Graphical Approach To College Algebra
- Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).arrow_forwardFind a basis for R2 that includes the vector (2,2).arrow_forwardUse a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forward
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