If M ( α ) = cos α sin α 0 − sin α cos α 0 0 0 1 ; M ( β ) = cos β 0 − sin β 0 1 0 sin β 0 cos β then [ M ( α ) M ( β ) ] − 1 is equal to -

Question

If M ( α ) = ​ cos α sin α 0 ​ − sin α cos α 0 ​ 0 0 1 ​ ​ ; M ( β ) = ​ cos β 0 − sin β ​ 0 1 0 ​ sin β 0 cos β ​ ​ then [ M ( α ) M ( β ) ] − 1 is equal to -

TestHub · Accepted Answer

​ [ M ( α ) M ( β ) ] − 1 = M ( β ) − 1 M ( α ) − 1 ] Now M( α ) − 1 = ​ cos α − sin α 0 ​ sin α cos α 0 ​ 0 0 1 ​ ​ = ​ cos ( − α ) sin ( − α ) 0 ​ − sin ( − α ) cos ( − α ) 0 ​ 0 0 1 ​ ​ = M ( − α ) M ( β ) − 1 = ​ cos β 0 sin β ​ 0 1 0 ​ − sin β 0 cos β ​ ​ = ​ cos ( − β ) 0 − sin ( − β ) ​ 0 1 0 ​ sin ( − β ) 0 cos ( − β ) ​ ​ = M ( − β ) [ M ( α ) M ( β ) ] − 1 = M ( − β ) M ( − α ) ​

Mathematics - Application of Derivative Question with Solution | TestHub

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