Let T be a linear transformation. Show that T is invertible by finding its standard matrix with Theorem 10. Then apply Theorem 8 to the standard matrix. Find its inverse. T(x1, x2, x3) = (−2x1 −7x2 −9x3, 2x1 + 5x2 + 6x3, x1 + 3x2 + 4x3)

Let T be a linear transformation. Show that T is invertible by finding its standard matrix with Theorem 10. Then apply Theorem 8 to the standard matrix. Find its inverse. T(x1, x2, x3) = (−2x1 −7x2 −9x3, 2x1 + 5x2 + 6x3, x1 + 3x2 + 4x3)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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Let T be a linear transformation. Show that T is invertible by finding its standard matrix with Theorem 10. Then apply Theorem 8 to the standard matrix. Find its inverse.

T(x1, x2, x3) = (−2x1 −7x2 −9x3, 2x1 + 5x2 + 6x3, x1 + 3x2 + 4x3)

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