Determine which of the matrices in Exercises 712 are orthogo

Determine which of the matrices in Exercises 7-12 are orthogonal. If orthogonal, find the inverse. 12. [ .5 .5 -.5 -.5 .5 .5 .5 .5 .5 -.5 -.5 .5 .5 -.5 .5 -.5] Determine which of the matrices in Exercises 7-12 are orthogonal. If orthogonal, find the inverse. 12. [.5 .5 -.5 -.5 .5 .5 .5 .5 .5 -.5 -.5 .5 .5 -.5 .5 -.5]

Solution

FOR AN ORTHOGONAL MATRIX , WE SHOULD HAVE DOT PRODUCT OF EACH PAIR OF COLUMN VECTORS SHALL BE ZERO THAT IS IF M = [V1 ,V2,V3,V4] ..THEN WE SHALL HAVE