Prove that:[ x y z ] ⎣⎡a hghbf gfc⎦⎤⎣⎡xyz⎦⎤=[ax2 +by2 +cz2+cfz+2gzx+2hxy]

Question

Prove that:[ x   y     z ] ⎣⎡​a hg​hbf ​gfc​⎦⎤​⎣⎡​xyz​⎦⎤​=[ax2 +by2 +cz2+cfz+2gzx+2hxy]

Filo · Accepted Answer

Let us consider the matrices as A , B , C which are the

1 \times 3, 3 \times 3, 3 \times 1

so that the matrix ABC will be

1 \times 1

Evidently they are comfortable for multiplication
ABC = A(BC) OR (AB ) C
(BC) =

⎣ ⎡ a x + h y + g z h x + b y + f z gx + f y + cz ⎦ ⎤_{3 \times 1}

ABC' = A (BC) n=

[x, y, z]_{1 \times 3,}

]

⎣ ⎡ a x + h y + g z h x + b y + f z gx + f y + cz ⎦ ⎤_{3 \times 1}

= [x (a x + h y + g z) + y (h x + b y f z) + z (gx + f y + cz)]_{1 \times 1,}

[a x^{2} + b y^{2} c z^{2} + 2 f yz + 2 g z x + 2 h x y]_{1 \times 1}

similarly we can find ABC as (AB)C are AB will be

1 \times 3,

and C being

3 \times 1

(AB) C will br

1 \times 1

matrix which will be same as above.

Question Text	Prove that: [ x y z ] $⎣ ⎡ a h g h b f g f c ⎦ ⎤$ $⎣ ⎡ x y z ⎦ ⎤$ $= [a x^{2} + b y^{2} + c z^{2} + c f z + 2 g z x + 2 h x y]$
Answer Type	Text solution:1
Upvotes	150

Prove that:
[ x y z ] $⎣ ⎡ a h g h b f g f c ⎦ ⎤$ $⎣ ⎡ x y z ⎦ ⎤$
$= [a x^{2} + b y^{2} + c z^{2} + c f z + 2 g z x + 2 h x y]$