Evaluate:(i) \(\begin{vmatrix}2&3&-2\\[0.3em]3&4&0\\[0.3em]1&-1&5\end

1.	Evaluate:(i) \(\begin{vmatrix}2&3&-2\\[0.3em]3&4&0\\[0.3em]1&-1&5\end{vmatrix}\)(ii) \(\begin{vmatrix}3&-1&2\\[0.3em]1&3&-2\\[0.3em]1&4&3\end{vmatrix}\)(iii) \(\begin{vmatrix}2&0&0\\[0.3em]0&4&0\\[0.3em]0&0&5\end{vmatrix}\)(iv) \(\begin{vmatrix}2&-1&1\\[0.3em]3&1&-2\\[0.3em]1&4&-1\end{vmatrix}\)(v) \(\begin{vmatrix}1&2&-1\\[0.3em]3&1&-4\\[0.3em]1&0&-2\end{vmatrix}\)
Answer» (i) \(\begin{vmatrix}2&3&-2\\[0.3em]3&4&0\\[0.3em]1&-1&5\end{vmatrix}\) 2(20 + 0) -3 (15 – 0) -2(-3 -4) 2(20) -3(15) -2(-7) 40 – 45 + 14 = 9 (ii) \(\begin{vmatrix}3&-1&2\\[0.3em]1&3&-2\\[0.3em]1&4&3\end{vmatrix}\) = 3(9+8) + 1(3 + 2) +2(4 – 3) = 3(17) + 1(5) + 2(1) = 51 + 5 + 2 = 58 (iii) \(\begin{vmatrix}2&0&0\\[0.3em]0&4&0\\[0.3em]0&0&5\end{vmatrix}\) 2(20 – 0) – 0 + 0 = 40 (iv) \(\begin{vmatrix}2&-1&1\\[0.3em]3&1&-2\\[0.3em]1&4&-1\end{vmatrix}\) 2(-1 + 8) + 1(-3 + 2) +1(12 – 1) 2(7) + 1(-1) +11 =14 – 1 + 11 = 24 (v) \(\begin{vmatrix}1&2&-1\\[0.3em]3&1&-4\\[0.3em]1&0&-2\end{vmatrix}\) = 1(-2 + 0) -2(-6 + 4) -1(0 – 1) = -2 – 2(-2) + 1 = -2 + 4 + 1 = 3.

Evaluate:(i) \(\begin{vmatrix}2&3&-2\\[0.3em]3&4&0\\[0.3em]1&-1&5\end{vmatrix}\)(ii) \(\begin{vmatrix}3&-1&2\\[0.3em]1&3&-2\\[0.3em]1&4&3\end{vmatrix}\)(iii) \(\begin{vmatrix}2&0&0\\[0.3em]0&4&0\\[0.3em]0&0&5\end{vmatrix}\)(iv) \(\begin{vmatrix}2&-1&1\\[0.3em]3&1&-2\\[0.3em]1&4&-1\end{vmatrix}\)(v) \(\begin{vmatrix}1&2&-1\\[0.3em]3&1&-4\\[0.3em]1&0&-2\end{vmatrix}\)

Answer»

(i) \(\begin{vmatrix}2&3&-2\\[0.3em]3&4&0\\[0.3em]1&-1&5\end{vmatrix}\)

2(20 + 0) -3 (15 – 0) -2(-3 -4)

2(20) -3(15) -2(-7)

40 – 45 + 14 = 9

(ii) \(\begin{vmatrix}3&-1&2\\[0.3em]1&3&-2\\[0.3em]1&4&3\end{vmatrix}\)

= 3(9+8) + 1(3 + 2) +2(4 – 3)

= 3(17) + 1(5) + 2(1)

= 51 + 5 + 2 = 58

(iii) \(\begin{vmatrix}2&0&0\\[0.3em]0&4&0\\[0.3em]0&0&5\end{vmatrix}\)

2(20 – 0) – 0 + 0 = 40

(iv) \(\begin{vmatrix}2&-1&1\\[0.3em]3&1&-2\\[0.3em]1&4&-1\end{vmatrix}\)

2(-1 + 8) + 1(-3 + 2) +1(12 – 1)

2(7) + 1(-1) +11 =14 – 1 + 11 = 24

(v) \(\begin{vmatrix}1&2&-1\\[0.3em]3&1&-4\\[0.3em]1&0&-2\end{vmatrix}\)

= 1(-2 + 0) -2(-6 + 4) -1(0 – 1)

= -2 – 2(-2) + 1 = -2 + 4 + 1 = 3.