Find `|A|` if `A=[{:(0,sinalpha,cosalpha),(sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}]`

Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alpha+delta)),(sinbeta,cosbeta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|

Find the amplitude of sinalpha+i(1-cosalpha)

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Find all possible real values of alpha satisfying the condition A_(alpha)+A_(alpha)" "^(T)=I.

lim_(alphato pi/4)(sinalpha-cosalpha)/(alpha-pi/4) is

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Show that A_(alpha)A_(beta)=A_(alpha+beta)

lim_(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))

Find the inverse of each of the matrices (if it exists ) {:[( 1,0,0),( 0 ,cos alpha , sin alpha ),( 0, sin alpha , -cos alpha ) ]:}

If F (alpha)= [{:(cosalpha,0, sinalpha),(0,1,0),(-sinalpha,0,cosalpha):}] Show that = F (alpha)^(-1)= F(-alpha)

Let lambdaa n dalpha be real. Find the set of all values of lambda for which the system of linear equations lambdax+(sinalpha)y+(cosalpha)z=0,x+(cosalpha)y+(sinalpha)z=0,-x+(sinalpha)y-(cosalpha)z=0. have trivial solution