Find the product :
`[ [ x,y,z]] [[a,h,g] ,[h,b,f],[ g,f,c ]] ((x),(y),(z))`

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

The order of [x,y,z],[(a,h,g),(h,b,f),(g,f,c)],[(x),(y),(z)] is (A) 3x1 (B) 1xx1 (C) 1xx3 (D) 3xx3

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

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

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

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 ' ')']|

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

I A=[x,y,z], B=[(a,h,g),(h,b,f),(g,f,c)] and C=[x,y,z]^T, then ABC is (A) not defined (B) a 1xx1 matrix (C) a 3xx3 matrix (D) none of these

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)