If D begin bmatrix 2 amp -1 amp 3 4 amp 1 amp 2... - JAMB Mathematics 2023 Question
If D = \(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)
Find |D|
A
16
B
14
C
-23
D
-37
correct option: c
The determinant (|D|) of a 3x3 matrix \(D = \begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\) is given by the formula:
\[ |D| = a(ei - fh) - b(di - fg) + c(dh - eg) \]
For the given matrix \(D = \begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\):
\[ |D| = 2(1 \cdot 1 - (-3) \cdot 2) - (-1)(4 \cdot 1 - 2 \cdot 1) + 3(4 \cdot (-3) - 1 \cdot 2) \]
\[ |D| = 2(1 + 6) + (4 - 2) + 3(-12 - 2) \]
\[ |D| = 2(7) + 2 - 3(14) \]
\[ |D| = 14 + 2 - 42 \]
\[ |D| = -26 \]
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