Find the value of determinant `[[a,h,g],[h,b,f],[g,f,c]]`

Evaluate the following: |[a,h,g],[h,b,f],[g,f,c]|

If A,B,C are matrices such that A=[x y z], B=[[a,h,g] , [h, b, f] , [g, f, c]] and C=[[x], [y], [z]] then find ABC

What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c):}][{:(x),(y),(z):}] ?

Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

If h(a)=h(b), the value of the integral int_a^b [f(g(h(x))]^(-1)f'(g(h(x)))g'(h(x))h'(x)dx is equal to

Find the area of the pentagon shown in Figure, if A D=10 c m ,\ A G=8c m ,\ A H=6c m ,\ A F=5c m ,\ B F=5c m ,\ C G=7c m\ a n d\ E H=3c mdot

If f,g, and h are differentiable functions of x and (delta) = |[f,g,h], [(xf)',(xg)',(xh)'],[(x^2f)' ',(x^2g)' ',(x^2h)' ']| prove that delta^(prime) = |[f,g,h],[f',g', h],[ (x^3f' ')',(x^3g' ')',(x^3h ' ')']|

Given the following equations and DeltaH^(@) values, determine the enthalpy of reaction at 298 K for the reaction : C_(2)H_(4)(g)+6F_(2)(g) to 2HF_(4)(g)+4HF(g) H_(2)(g)+F_(2)(g)to2HF(g)+2HF(g)," "DeltaH_(1)^(@)=-537" kJ" C(s)+2F_(2)(g)toCF_(4)(g)," "DeltaH_(2)^(@)=-680" kJ" 2C(s)+2H_(2)(g)toC_(2)H_(4)(g)," "DeltaH_(3)^(@)=52" kJ"

If f,g , and h are differentiable functions of x and "delta"=|[f,g,h],[(xf)',(xg)',(x h)'],[(x^2f)' ',(x^2g)' ',(x^2h)' ']| prove that "delta"^(prime)=|[f,g,f],[f',g', h '],[(x^3f' ')',(x^3g' ')',(x^3h ' ')']|

If A=[ x y z],B=[(a,h,g),(h,b,f),(g ,f,c)],C=[alpha beta gamma]^T then ABC is