Evaluate : [(29,26,22),(25,31,27),(63,54,46)]

Question

Evaluate : 

\(\begin{bmatrix} 29 & 26& 22 \\[0.3em] 25 & 31 &27 \\[0.3em] 63 & 54 & 46 \end{bmatrix}\)

[(29,26,22),(25,31,27),(63,54,46)]

Answer 1

\(\begin{vmatrix} 29 & 26& 22 \\[0.3em] 25 & 31 &27 \\[0.3em] 63 & 54 & 46 \end{vmatrix}\) 

= \(\begin{vmatrix} 4 & -5 & -5 \\[0.3em] 25 & 31 &27 \\[0.3em] 63 & 54 & 46 \end{vmatrix}\) [R₁’ = R₁ - R₂]

=  \((\frac{1}{2})\) \(\begin{vmatrix} 4 & -5 & -5 \\[0.3em] 25 & 31 &27 \\[0.3em] 63 & 54 & 46 \end{vmatrix}\) [R₂’ = 2R₂]

= \((\frac{1}{2})\) \(\begin{vmatrix} 4 & -5 & -5 \\[0.3em] 25 & 31 &27 \\[0.3em] 63 & 54 & 46 \end{vmatrix}\) [R₂’ = R₂ - R₃]

= \(\begin{vmatrix} 4 & -5 & -5 \\[0.3em] -13 & 8 &8 \\[0.3em] 63/2 & 27 & 23 \end{vmatrix}\)[R₃’ = 2R₃]

= 4(8 × 23 - 8 × 27) - 5{8 × 63/2 - ( - 13) × 23} - 5{( - 13) × 27 - 8 × } 

[expansion by first row]

= 132