38 EXERCISES (26) Grive proofs for all properties of the matrix transpose. Show that if A&M...

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38 EXERCISES (26) Grive proofs for all properties of the matrix transpose. Show that if A&M₂ (B) is symmetric and non-s then At is also symmetric. (28) Let A.BE Mu (IR). Show that A, B, AB symmetric ⇒AB=BA. 29 Giren A, PEM₂ (R), show that A symmetric =B=PTAP symmetric 30 Consider the rotation matrix 8(81= [ cost -sing] non-singular, sind cose a) Show that R(8? is non-singular with [R(S)] = R(-9) 6) Show that [RC]T = R(-9) c) For what angles Jeth is Ri(d) symmetric? 38 EXERCISES (26) Grive proofs for all properties of the matrix transpose. Show that if A&M₂ (B) is symmetric and non-s then At is also symmetric. (28) Let A.BE Mu (IR). Show that A, B, AB symmetric ⇒AB=BA. 29 Giren A, PEM₂ (R), show that A symmetric =B=PTAP symmetric 30 Consider the rotation matrix 8(81= [ cost -sing] non-singular, sind cose a) Show that R(8? is non-singular with [R(S)] = R(-9) 6) Show that [RC]T = R(-9) c) For what angles Jeth is Ri(d) symmetric?