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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Matrices

NDA 2016 · Mathematics · Matrices

What is [ array lll x & y & z array ][ array lll a & h & g h & b &...

What is \left[xyz\begin{array}{lll}x & y & z\end{array}\right]\left[ahghbfgfc\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right] equal to?

Options

  1. A[ax+hy+gzh+b+fg+f+c][\mathrm{ax}+\mathrm{hy}+\mathrm{gz} \mathrm{h}+\mathrm{b}+\mathrm{f} \quad \mathrm{g}+\mathrm{f}+\mathrm{c}]
  2. B\left[ahghxbyfzgfc\begin{array}{lcr}\mathrm{a} & \mathrm{h} & \mathrm{g} \\ \mathrm{hx} & \mathrm{by} & \mathrm{fz} \\ \mathrm{g} & \mathrm{f} & \mathrm{c}\end{array}\right]
  3. C\left[ax+hy+gzhx+by+fzgx+fy+cz\begin{array}{l}\mathrm{ax}+\mathrm{hy}+\mathrm{gz} \\ \mathrm{hx}+\mathrm{by}+\mathrm{fz} \\ \mathrm{gx}+\mathrm{fy}+\mathrm{cz}\end{array}\right]
  4. D\left[[ax+hy+gzhx+by+fzgx+fy+cz]\begin{array}{llll}{[a x+h y+g z} & h x+b y+f z & g x+f y+c z]\end{array}\right.

Correct answer

D. \left[[ax+hy+gzhx+by+fzgx+fy+cz]\begin{array}{llll}{[a x+h y+g z} & h x+b y+f z & g x+f y+c z]\end{array}\right.

Step-by-step solution

[xyz][ahghbfgfc]=[ax+hy+gzhx+by+fzgx+fy+cz]\begin{aligned} & {\left[\begin{array}{lll}x & y & z\end{array}\right]\left[\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right]} \\ & =[a x+h y+g z \quad h x+b y+f z \quad g x+f y+c z]\end{aligned}
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