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JAMB Mathematics 2024 Paper

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Question : 1

Total: 50

Evaluate the determinant of the matrix M =

\begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}

20
25
30
35

Solution:

Concept:

Determinant of a

3 \times 3

matrix using expansion along the first row.

Explanation:

For

M = \begin{bmatrix}3 & 4 & 6\\2 & 1 & -1\\-1 & 3 & 5\end{bmatrix}

, expand along the first row.

|M| = 3\begin{vmatrix}1 & -1\\3 & 5\end{vmatrix} - 4\begin{vmatrix}2 & -1\\-1 & 5\end{vmatrix} + 6\begin{vmatrix}2 & 1\\-1 & 3\end{vmatrix}

Evaluate each

2 \times 2

determinant:

3(1 \times 5 - (-1) \times 3) = 3(5 + 3) = 3 \times 8 = 24

-4(2 \times 5 - (-1) \times (-1)) = -4(10 - 1) = -4 \times 9 = -36

6(2 \times 3 - 1 \times (-1)) = 6(6 + 1) = 6 \times 7 = 42

Add the results:

24 - 36 + 42 = 30

Answer:

\boldsymbol{30}

Thus, the correct option is C.

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