Q157 / 270 · NDA 2016 (Phase 2) · Mathematics

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

  • A
    $[\mathrm{ax}+\mathrm{hy}+\mathrm{gz} \mathrm{h}+\mathrm{b}+\mathrm{f} \quad \mathrm{g}+\mathrm{f}+\mathrm{c}]$
  • B
    $\left[\begin{array}{lcr}\mathrm{a} & \mathrm{h} & \mathrm{g} \\ \mathrm{hx} & \mathrm{by} & \mathrm{fz} \\ \mathrm{g} & \mathrm{f} & \mathrm{c}\end{array}\right]$
  • C
    $\left[\begin{array}{l}\mathrm{ax}+\mathrm{hy}+\mathrm{gz} \\ \mathrm{hx}+\mathrm{by}+\mathrm{fz} \\ \mathrm{gx}+\mathrm{fy}+\mathrm{cz}\end{array}\right]$
  • Correct answer
    D
    $\left[\begin{array}{llll}{[a x+h y+g z} & h x+b y+f z & g x+f y+c z]\end{array}\right.$

Solution

$\begin{aligned} & {\left[\begin{array}{lll}x & y & z\end{array}\right]\left[\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right]} \\ & =[a x+h y+g z \quad h x+b y+f z \quad g x+f y+c z]\end{aligned}$

Hence, the correct answer is option: 'D'.

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