If A is an arbitrary vector and R and S are arbitrary dyads, verify that: (a) (I x A) R = A x R. (c) (Rx A)¹ = -Ax RT. (b) (A x I) R = A x R. (d) (R.S)¹ = ST.RT.

Elementary Linear Algebra (MindTap Course List)
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Chapter6: Linear Transformations
Section6.5: Applications Of Linear Transformations
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2.47 If A is an arbitrary vector and R. and S are arbitrary dyads, verify that:
(b) (A x I) R = A x R.
(a) (I x A) R = A x R.
(c) (R x A)T = -A x R¹.
(e) (R-S)-¹ S-¹.R-¹.
T
(d) (RS)
ST . R¹.
(f) (RS)-T=R-T.S-T.
=
=
Transcribed Image Text:2.47 If A is an arbitrary vector and R. and S are arbitrary dyads, verify that: (b) (A x I) R = A x R. (a) (I x A) R = A x R. (c) (R x A)T = -A x R¹. (e) (R-S)-¹ S-¹.R-¹. T (d) (RS) ST . R¹. (f) (RS)-T=R-T.S-T. = =
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