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State true or false. If A, B, C are three matrices such that

Question

State true or false.
If $A, B, C$ are three matrices such that
$A = [x y z],$ $B = ⎣ ⎡ a h g h b f g f c ⎦ ⎤$ and $C = ⎣ ⎡ x y z ⎦ ⎤,$ then $A BC = [a x^{2} + b y^{2} + c z^{2} + 2 h x y + 2 g z x + 2 f yz]$

True

False

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State true or false.

A, B, C

are three matrices such that

A = [x y z],

B = ⎣ ⎡ a h g h b f g f c ⎦ ⎤

and

C = ⎣ ⎡ x y z ⎦ ⎤,

then

A BC = [a x^{2} + b y^{2} + c z^{2} + 2 h x y + 2 g z x + 2 f yz]

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Text solutionVerified

Given,

A, B, C

are three matrices such that

A = [x y z],

B = ⎣ ⎡ a h g h b f g f c ⎦ ⎤

and

C = ⎣ ⎡ x y z ⎦ ⎤

Consider,

A B = [x yz] ⎣ ⎡ a h g h b f g f c ⎦ ⎤

\Rightarrow

= [a x + y h + z g x h + y b + zc xg + y f + zc]

Now,

A BC = [a x + y h + z g x h + y b + zc xg + y f + zc] ⎣ ⎡ x y z ⎦ ⎤

\Rightarrow

= [a x^{2} + x y h + z gx + x h y + y^{2} h + zcy + xg z + y f z + z^{2} c]

Hence it's true

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Question Text	State true or false. If $A, B, C$ are three matrices such that $A = [x y z],$ $B = ⎣ ⎡ a h g h b f g f c ⎦ ⎤$ and $C = ⎣ ⎡ x y z ⎦ ⎤,$ then $A BC = [a x^{2} + b y^{2} + c z^{2} + 2 h x y + 2 g z x + 2 f yz]$
Answer Type	Text solution:1
Upvotes	150