If the matrix M = \begin{pmatrix} 2x & 4 \\ 3 & 6 \end{pmatrix} is a singular matrix, what… — JAMB UTME

If the matrix $M = \begin{pmatrix} 2x & 4 \\ 3 & 6 \end{pmatrix}$ is a singular matrix, what is the value of $x$ ?

The value of

x

1

A matrix is singular when its determinant equals zero. Evaluating the determinant of

\begin{pmatrix} 2x & 4 \\ 3 & 6 \end{pmatrix}

gives

(2x)(6) - (4)(3) = 12x - 12

. Setting

12x - 12 = 0

leads directly to

x = 1

Recall the condition for a matrix to be singular.

A matrix is singular if and only if its determinant is equal to zero, so

\det(M) = 0

Singular matrices have no inverse because their determinant is zero.

Calculate the determinant of matrix

M = \begin{pmatrix} 2x & 4 \\ 3 & 6 \end{pmatrix}

\det(M) = (2x)(6) - (4)(3) = 12x - 12.

The determinant of a

2 \times 2

matrix

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

ad - bc

Set the determinant equal to zero and solve for

x

12x - 12 = 0 \implies 12x = 12 \implies x = 1

Solving the linear equation yields the required parameter value.

Condition for Singular Matrix and 2x2 Determinant Evaluation

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