Given that the determinant of the 3 \times 3 matrix M = \begin{pmatrix} 3 & 1 & 0 \\ 2 & x… — JAMB UTME

Given that the determinant of the $3 \times 3$ matrix $M = \begin{pmatrix} 3 & 1 & 0 \\ 2 & x & -1 \\ 0 & 4 & 2 \end{pmatrix}$ is equal to $20$ , calculate the value of $x$ .

Answer: 2

Answer

The value of

x

2

Expanding the matrix

M

along its top row yields

\det(M) = 3(2x + 4) - 1(4) = 6x + 8

. Setting this expression equal to

20

gives

6x + 8 = 20

, which simplifies to

6x = 12

, yielding

x = 2

Step-by-Step Solution

Expand the 3x3 matrix along the first row

\det(M) = 3(2x - (-4)) - 1(4 - 0) + 0

Cofactor expansion along a row containing a zero simplifies the computation of a 3x3 determinant.

Simplify the algebraic expression for the determinant

\det(M) = 6x + 8

Distribute the coefficients and combine like constant terms.

Solve the linear equation for x

x = 2

Subtract 8 from 20 to get 12, then divide by 6.

Key Concept

Determinant of a 3x3 Matrix via Cofactor Expansion

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