Use the relationships between A , B , and C and A ' , B ' , and C ' on page 960 to show that A + C is invariant under rotation. That is, show that A + C = A ' + C ' .
Use the relationships between A , B , and C and A ' , B ' , and C ' on page 960 to show that A + C is invariant under rotation. That is, show that A + C = A ' + C ' .
Solution Summary: The author explains how to prove that A+C is invariant using relationship between B and C.
Use the relationships between
A
,
B
,
and
C
and
A
'
,
B
'
,
and
C
'
on page
960
to show that
A
+
C
is invariant under rotation. That is, show that
A
+
C
=
A
'
+
C
'
.
When A is multiplied by a plane rotation Qij, which entries of A are changed? When QiJA is multiplied on the right by Q-;/, which entries are changed now?
Prove that the reflection along the line y = −x is equivalent to reflection along the
y-axis followed by a counter-clockwise rotation by 90◦
.
Show that a counterclockwise rotation in R^2 through an angle α is described by the matrix
Rα = (cos α − sin α) (sin α cos α)
University Calculus: Early Transcendentals (4th Edition)
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